Title   name Lastest   |   Most hits   년도선택 최근 50건20192018201720162015201420132012201120102009200820072006200520042003200220012000     The Arithmetic of Function Fields and Related Topics Class groups under relative quadratic extensions Qin Yue (Nanjing Univ. of Astronautics and Aeronautics) 2013-02-21   Let $E$ be a relative quadratic extension of a number field $F$, the 2-Sylow subgroup of the class group of $F$ elementary abelian, and the $S$-ideal class number of $F$ odd, where $S$ is a set consisting of all infinite primes and some finite primes of $F$ ramifying in $E$. In this paper, we compute the 2-rank and 4-rank of the class group of $E$.   The Arithmetic of Function Fields and Related Topics Some Results on Harmonic Analysis on Siegel-Jacobi Space Jae-Hyun Yang (Inha Univ.) 2013-02-21   The Jacobi group, the semi-direct product of the symplectic group and the Heisenberg group is one of the simplest and most important examples of a non-reductive Lie group. Its associated non-reductive homogeneous space is the so-called Siegel-Jacobi space that is very important arithmetically and geometrically. In this lecture, I develop the theory of harmonic analysis on the Siegel-Jacobi space. I plan to introduce some results about harmonic analysis on the Siegel-Jacobi space obtained by J.-H. Yang, E. Balslev, F. Gay-Balmaz, C. Tronci, S. Berceanu, A. Gheorge, H. Ochiai and M. Itoh.   The Arithmetic of Function Fields and Related Topics The maximum weight of cross-t intersecting families Sang June Lee (KAIST) 2013-02-21   A central result in extremal combinatorics is textit{the ErdH os--Ko--Rado Theorem} which investigates the maximum size of $cA subset binom{[n]}{k}$ such that for every choice of sets $A_1, A_2in cA$ we have $|A_1cap A_2| geq t$. In this talk we consider a version with two families. Two families $cA$ and $cB subset binom{[n]}{k}$ are {em cross $t$-intersecting} if for every choice of sets $A in cA$ and $B in cB$ we have $|A cap B| geq t$. The following `cross $t$-intersecting version' of the ErdH os-Ko-Rado Theorem was conjectured: For all $n geq (t+1)(k-t+1)$ the maximum value of $|cA||cB|$ for two cross $t$-intersecting families $cA, cB subsetbinom{[n]}{k}$ is $binom{n-t}{k-t}^2$.We verified a strongly related textit{$p$-weighted version} of the above conjecture for $t geq 14$. For $0   The Arithmetic of Function Fields and Related Topics Diophantine approximation in fields of formal power series over finite fields. Huei Jeng Chen (Academia Sinica) 2013-02-20   For any positive integer n and real number λ >= 1, let K_n(λ) be the set of all real numbers Ɵ such that for any λ’<λ, there exist infinitely many algebraic numbers α with degree at most n satisfying | Ɵ -α| < H(α)-(n+1)λ’. Moreover we let Kn ‘(λ) be the subset of Kn (λ) consisting of all Ɵ not in Kn (λ’) for any λ’<λ. Baker and Schmidt proved that the Hausdorff dimensions of Kn (λ) and Kn ‘(λ) are both 1/λ. We will give similar results of Baker and Schmidt in function field version.   The Arithmetic of Function Fields and Related Topics Drinfeld modular forms and modular representation theory Ernst Urlich Gekeler (Saarland Univ.) 2013-02-20   Let Gamma(T) be the full congruence subgroup of level T in the Drinfeld modular group Gamma:=GL(2, F_q[T]). We (joint work with my PhD student Enrico Varela) consider the ring of modular forms Gamma(T) as a module under the quotient group G=Gamma/Gamma(T), which is isomorphic with GL(2,F_q). We have some results about Jordan-Hölder series of the space of forms of fixed weight k, considered as a G-module.   The Arithmetic of Function Fields and Related Topics Moebius function in short intervals for function fields Hwanyup Jung (Chungbuk National Univ.) 2013-02-20   Let be the Möbius function on the polynomial ring Fq[T] over the nite field Fq of q elements. We compute the (asymptotic) mean value and variance of Möbius function in short intervals as $q-> infty$   The Arithmetic of Function Fields and Related Topics On automorphisms of prime order of Riemann surfaces, function fields, or algebraic curves Andreas Schweizer (KAIST) 2013-02-20   Let X be a compact Riemann surface (or equivalently, a function field over the complex numbers, or equivalently a smooth projective curve over the complex numbers) of genus at least 2. A cyclic subgroup of prime order p of Aut(X) is called properly (p,h)-gonal if it has a fixed point and the quotient surface has genus h. We show that if p>6h+6>11, then a properly (p,h)-gonal subgroup of Aut(X) is unique.   The Arithmetic of Function Fields and Related Topics Optimal quotients of Mumford curves and component groups Mihran Papikian (Penn. State Univ.) 2013-02-20   Let $X$ be a Mumford curve. We say that an elliptic curve is an optimal quotient of $X$ is there is a finite morphism $Xto E$ such that the homomorphism $pi: Jac(X)to E$ induced by the Albanese functoriality has connected and reduced kernel. We consider the functorially induced map $pi_ast: Phi_Xto Phi_E$ on component groups of the Neron models of $Jac(X)$ and $E$. We show that in general this map need not be surjective, which answers negatively a question of Ribet and Takahashi. Using rigid-analytic techniques, we give some conditions under which $pi_ast$ is surjective, and discuss arithmetic applications to modular curves. This is a joint work with Joe Rabinoff.   The Arithmetic of Function Fields and Related Topics Theta constant of odd levels Ick Sun Eum (KAIST) 2013-02-20   We provide the necessary and sufficient condition for the modularity of certain product of theta constants of given odd levels.   The Arithmetic of Function Fields and Related Topics Automorphic forms of Drinfeld type and the basis problem. Jing Yu (National Taiwan Univ.) 2013-02-19   For any function field k, together with a fixed place called the infinity, we give explicit construction of ''heta series'' from Eichler orders of definite quaternion algebra over k. These theta series are recognized as automorphic forms of Drinfeld type for GL2 over k. Description of the space generated by these theta series inside all Drinfeld type automorphic forms is given. This gives an answer to the basis problem for Drinfeld type automorphic forms.   The Arithmetic of Function Fields and Related Topics Canonical models of modular curves Changheon Kim (Hanyang Univ.) 2013-02-19   Modular curves parametrize elliptic curves with prescribed torsion structures. In this talk I will investigate torsion of elliptic curves over number fields by applying canonical models of modular curves.   The Arithmetic of Function Fields and Related Topics Determining Whitmans generalized cyclotomic numbers of order 4 Xiao-Meng Zhu (Nanjing Univ. of Astronautics and Aeronautics) 2013-02-19   Let $p$ and $q$ be distinct primes with $gcd(p-1,q-1)=4$, Whiteman gave the sixteen cyclotomic numbers depending solely upon one of the two decompositions: $pq=a^2+4b^2=a'^2+4b'^2, aequiv a'equiv 1pmod 4$. In this paper, we will determine the sixteen cyclotomic numbers of order four depending on unique $a, b$ if we choose a common primitive root of $p$ and $q$.   The Arithmetic of Function Fields and Related Topics Explicit isogeny theorems and different bounds of Drinfeld modules Yoonjin Lee (Eewha Women Univ.) 2013-02-19   Given two non-isogenous rank $r$ Drinfeld $A$-modules $phi$ and $phi'$ over $K$, where $F = F_q(T)$, $A = F_q[T]$, and $K$ is a finite extension of $F$, we obtain a partially explicit upper bound (dependent only on $phi$ and $phi'$) on the degree of primes $p$ of $K$ such that $P_p(phi) not= P_p(phi')$, where $P_p(ast)$ denotes the characteristic polynomial of Frobenius at $p$ on a Tate module of $ast$. The bounds are completely explicit in terms of the defining coefficients of $phi$ and $phi'$, except for one term, which can be made explicit in the rank 2 case by determining the Newton polygons of exponential functions attached to $phi$ and the successive minima of the lattice associated to $phi$ by uniformization. An ingredient in the proof of the explicit isogeny theorem for general rank is an explicit bound for the different divisor of torsion fields of Drinfeld modules which detects primes of potentially good reduction.   The Arithmetic of Function Fields and Related Topics Rational points on curves over finite fields and Drinfeld modular varieties Alp Bassa (Sabanci Univ.) 2013-02-19   In the past modular curves of various type (classical, Drinfeld, Shimura) have been used successfully to construct high genus curves with many rational points over finite fields of square cardinality. In this talk I will explain how Drinfeld modular varieties can be used similarly to obtain high genus curves over any non-prime finite field with many rational points. This way we obtain lower bounds for the Ihara constant A(q) for all non-prime q, which are better then all previously known bounds.   The Arithmetic of Function Fields and Related Topics Shift operators and two applications to $Fq[[T]]$ Sangtae Jeong (Inha Univ.) 2013-02-19   This talk comprises two applications of shift operators to characterization of continuous functions and ergodic functions defined on the integer ring of a non-Archimedean local field of positive characteristic. In the first part of the talk, we establish that digit expansion of shift operators becomes an orthonormal basis for the space of continuous functions on ${F}_q[[T]],$ including a closed-form expression for expansion coefficients, and we establish that this is also true for $p$-adic integers, excluding the coefficient formula. In the second part, we obtain the necessary and sufficient conditions for ergodicity of 1-Lipschitz functions represented on ${F}_2[[T]]$ by digit shift operators, recalling the cases with the Carlitz polynomials and digit derivatives.   The Arithmetic of Function Fields and Related Topics Counting dihedral and quaternionic extensions in function fields Jaehyun Ahn (Chungnam National Univ.) 2013-02-18   We give asymptotic formulas for the number of biquadratic extensions of $F_q[T]$ that admit a quadratic extension which is a Galois extension of $F_q[T]$ with a prescribed Galois group.   The Arithmetic of Function Fields and Related Topics Infinite families of elliptic curves over Dihedral quartic number fields Daeyeol Jeon (Kongju Univ.) 2013-02-18   In this talk, we construct infinite families of elliptic curves over quartic number fields with torsion group $mathbb Z/Nmathbb Z$ with $N = 20,24$. Moreover, we prove that for each elliptic curve $E_t$ in the constructed families, the Galois group $Gal(L/mathbb Q)$ is isomorphic to the Dihedral group $D_4$ of order 8 for the Galois closure $L$ of $K$ over $mathbb Q$, where $K$ is the defining field of $(E_t ,Q_t)$ and $Q_t$ is a point of $E_t$ of order $N$.   The Arithmetic of Function Fields and Related Topics On A-expansions of Drinfeld modular forms and vectorial Drinfeld modular forms. Alexandar Petrov (Texas A and M at Qatar) 2013-02-18   In this talk we will present recent results that show the existence of infinitely many cuspidal Drinfeld eigenforms that possess A-expansions. In addition, we will give examples (some of which conjectural) of vectorial Drinfeld modular forms with A-expansions.   The Arithmetic of Function Fields and Related Topics On congruences of Galois representations of global fields Yuichiro Taguchi (Kyushu Univ.) 2013-02-18   We give a simple criterion for two v-adic Galois representations of a global field K to be locally isomorphic at another place u in terms of their reductions mod v. Such a study is motivated by the Rasmussen-Tamagawa conjecture for Abelian varieties.   The Arithmetic of Function Fields and Related Topics The zeros of certain weakly holomorphic Drinfeld modular forms Soyoung Choi (Dongguk Univ.) 2013-02-18   Let $k$ be an integer such that $kequiv 0 pmod {q-1}$. Then there exist unique integers $l_k$ and $r_k$ such that $0leq r_kleq q$ and $k=(q^2-1)l_k +(q-1)r_k$. For each integer $mgeq-l_k$,there exists a unique weakly holomorphic Drinfeld modular form $f_{k,m}$ of weight $k$ for $GL_2(A)$ with a $t$-expansion of the form begin{equation*}f_{k,m}(z)=t^{-(q-1)m} +O(t^{(q-1)(l_k+1)}) end{equation*}. In this talk, we review some properties of these forms $f_{k,m}$ and prove that the zeros of $f_{k,m}(z)$ in the fundamental domain $frak{F}$ are on the unit circle $|z|=1$ under a certain condition and in addition, if $q$ is odd then the zeros of $f_{k,m}$ are transcendental over $K$ or elliptic points. Where $frak{F}:={zin Omega~:~ |z|=text{inf}{|z-a|~ : ~ a in Bbb{F}_q[T]}geq 1}$. This is a work with Bohae Im We verified a strongly related textit{$p$-weighted version} of the above conjecture for $t geq 14$. For $0   The Arithmetic of Function Fields and Related Topics Average values of L-functions in function fields Jung, Hwanyup (Chungbuk National University) 2011-08-19   Gauss made two famous conjectures about average values of class numbers of orders in quadratic number fields, which were proven by Lipschitz and Siegel. In quadratic function field cases, such average values formulas were obtained by Hoffstein and Rosen in odd characteristic and Chen in even characteristic. Rosen also obtained such a formula in (cubic) Kummer extension case. In this talk, we will introduce our recent result about average values of class numbers of orders in (cubic) Artin-Schreier extensions. We also will talk about average values of Dirichlet L-series with prime conductors in function field case.   The Arithmetic of Function Fields and Related Topics Basis for the space of weakly holomorphic modular forms in higher level cases and its application Kim, Changheon (Hanyang University) 2011-08-19   (joint work with Soyoung Choi) Let $Gamma_0^+(p)$ be the group generated by the Hecke group $Gamma_0(p)$ and the Fricke involution $W_p$. In this talk I will construct a canonical basis for the space of weakly holomorphic modular forms of integral weight for $Gamma_0^+(p)$ and investigate its properties and applications   The Arithmetic of Function Fields and Related Topics Boundary maps to the supersingular points and the evaluation of Drinfeld modular Beilinson-Kato type elements Satoshi Kondo (IPMU) 2011-08-19   We consider an analogue of Beilinson-Kato type elements in the K-theory of the moduli of Drinfeld modular varieties. We compute the value at supersingular points via successive boundary maps (in the localization sequences obtained from the strata).  This is a Drinfeld modular analogue of one of first steps in the proof by Beilinson as presented by Schappacher and Scholl of integrality of Beilinson elements.By restricting to Beilinson-Kato type elements (and not considering all of the Beilinson type elements),we prove a similar statement by explicit computation, which then generalizes to higher dimensions.   The Arithmetic of Function Fields and Related Topics Classification of bielliptic modular curves Jeon, Daeyeol (Kongju National University) 2011-08-19   An algebraic curve $X$ is called {it bielliptic} if it admits a map from $X$ to an elliptic curve $E$ of degree 2. In this talk, we present a classification of bielliptic certain modular curves.   The Arithmetic of Function Fields and Related Topics Hilbert genus fields of real biquadratic fields Qin Yue (Nanjing University of Aeronautics and Astronautics) 2011-08-19   Let be a real biquadratic field with p ≡ 1mod 4 or p = 2, and d a squarefree positive integer. The Hilbert genus field is described explicitly by Yue (Ramanujan J. 21:17–25, 2010) in the case that p ≡ 1 mod 4 and d ≡ 3 mod 4. In this article, we give the Hilbert genus field of K explicitly for the remaining cases. We also consider the function field analogue of this problem.   The Arithmetic of Function Fields and Related Topics Diophantine Approximation in function fields Dinesh Thakur (University of Arizona) 2011-08-18   While Roth's famous theorem says that Diophantine approximation exponent for algebraic numbers is 2, the corresponding situation in function fields is not even conjecturally understood. We will describe the recent advances in understanding these issues.   The Arithmetic of Function Fields and Related Topics Drinfeld modular forms and modular representation theory Ernst Urlich Gekeler (Saarlandes University) 2011-08-18   Let Gamma(T) be the full congruence subgroup of level T in the Drinfeld modular group Gamma:=GL(2, F_q[T]). We (joint work with my PhD student Enrico Varela) consider the ring of modular forms Gamma(T) as a module under the quotient group G=Gamma/Gamma(T), which is isomorphic with GL(2,F_q). We have some results about Jordan-Hölder series of the space of forms of fixed weight k, considered as a G-module.   The Arithmetic of Function Fields and Related Topics Gauss sums over some matrix groups and their applications Yan Li (Agriculture University) 2011-08-18   In this talk, we give explicit expressions of Gauss sums for general (resp. special) linear groups over nite elds, which involve classical Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups, i.e, the subgroup of upper triangular matrices. Furthermore, we give the following three applications: (1) the number of invertible matrices of zero-trace over nite elds has been counted. (2) two bounds by Ferguson, Homan, Luca, Ostafe and Shparlinski in [Some additive combinatorics problems in matrix rings, Rev. Mat. Complut. (23) 2010, 501{513 ] have been largely improved. (3) several uniformly distributed results in matrix groups have been presented. Finally, if the time is enough, I will also explain the applications of Gauss sums over some matrix groups in coding and cryptography which connect to Dae San Kim's recent work in [ D. S. Kim, Codes associated with special linear groups and power moments of multi-dimensional Kloosterman sums, Ann. Mat. Pura Appl. (4) 190 (2011), 61{76]. These are joint work with Su Hu.   The Arithmetic of Function Fields and Related Topics On metaplectic forms over function fields and an analogue of Waldspurger's formula Fu-Tsun Wei (National Tsinghua University) 2011-08-18   In this talk, I present a concept of half integral weight in the function field context. I also introduce a Shimura-type map from the space of weight 2 automorphic forms to the space of weight 3/2 metaplectic forms. From the central critical value formula of Rankin-type L-series attached to weight 2 newforms, these special values are essentially Fourier coefficients of corresponding weight 3/2 forms. This is a function field analogue of Waldspurger's formula   The Arithmetic of Function Fields and Related Topics A class of algebraic differential equation that the Iwasawa power series does not satisfy Sun, Haesang (Chungbuk National University) 2011-08-17   Due to universality theorem, Dirichlet L-function does not satisfy any non-trivial algebraic differential equations. In the talk, we establish the conjectural analogue for the Iwasawa power series and present a class of algebraic differential equations that the Iwasawa power series does not satisfy.   The Arithmetic of Function Fields and Related Topics A p-adic view of multiple power sums Kim, Minsoo (KAIST) 2011-08-17   Washington [p-adic L-functions and sums of powers, J. Number Theory  69 (1998), 50--61] gave an explicit p-adic expansion of  the harmonic  series as a p-adic power series. The coefficients are values of p-adic L-functions. In this talk, we gave an explicit p-adic expansion of the multiple harmonic  series as a p-adic power series. The coefficients are values of multiple two-variable p-adic L-functions. Washington's formula is a special case of the  formula given in this talk. These are joint work with Su Hu.   The Arithmetic of Function Fields and Related Topics Entire functions sharing simple a-points with their first derivative Andreas Schweizer (Academia Sinica) 2011-08-17   Let f be an entire function in the complex plane. A famous theorem by Mues and Steinmetz says that if for two complex numbers a_{1} and a_{2} the function f and its derivative f^{'} take the value a_i at exactly the same points of the complex plane, then ff^{'}, that is f(z) = Ce^{z}. We discuss what happens if we only know that the points where f respectively f^{‘} takes the value ai with multiplicity one are exactly the same. The proof also uses function eld arguments.   The Arithmetic of Function Fields and Related Topics Fermat quotient operators and locally analytic functions Jeong, Sangtae (Inha University) 2011-08-17   Recently, Buium et al. characterize locally analytic functions on $Z_p$ in terms of a restricted power series over $Z_p$ in finitely  many iterates of the Fermat quotient operator. In this talk we establish the function field analogue of their result: Let $R:=F[[p]]$ be  the ring of formal power series in one variable $p$ over a finite field $F$ of size $q$ and $d: R rightarrow R$ be the Fermat quotient operator defined by $d x = {(x-x^q)}/{p}.$ Then we prove that a function $f: R rightarrow R$  is locally analytic of order $m$ if and only if there exists an integer $m geq0$ so that $f(x)=F(x, d x, cdots, d^m x),$ where $F$ is a restricted power series in $R[[x_0, cdots, x_m]].$ In addition, we deduce Wagner's result for continuous functions on completions of $F_r[T].$.   The Arithmetic of Function Fields and Related Topics Maass-Jacobi Forms Yang, Jaehyun (Inha University) 2011-08-17   In this talk, I introduce the notion of Maass-Jacobi forms and study some properties of Maass-Jacobi forms. I also deal with invariant differential operators on Siegel-Jacobi space and present some important problems. I mention some results of Kathrin Bringmann and her colleagues about Maass-Jacobi forms.   The Arithmetic of Function Fields and Related Topics Note on the relation between prime generating polynomials and class number one problem for some number fields Lee, Joonho (Seoul National University) 2011-08-17   It has been known for a long time that there exists the close connection between prime generating polynomials and class number one problem for some number fields. In this talk, we explain about known results for quadratic number fields and introduce some results and problems related to this topic for cubic fields.   The Arithmetic of Function Fields and Related Topics On p-adic Hurwitz-type Euler zeta functions Su Hu (KAIST) 2011-08-17   The definition for the p-adic Hurwitz-type Euler zeta functions has been given by using the fermionic p-adic integral on Zp. By computing the values of this kind of p-adic zeta function at negative integers, we show that it inter-polates the Euler polynomials p-adically. Many properties are provided for the p-adic Hurwitz-type Euler zeta functions, including the convergent Laurent series expansion, the distribution formula, the functional equation, the re리ection formula, the derivative formula, the p-adic Raabe formula and so on. The definition for the p-adic Euler L-functions has also been given by using the p-adic Hurwitz-type Euler zeta functions. These is a joint work with Min-Soo Kim.   The Arithmetic of Function Fields and Related Topics On t-modules Jing Yu (National Taiwan University) 2011-08-17   I will give a survey on t-modules, and the associated t-motives. Discuss the periods of t-modules, and the related transcendence theory. We shall also compare t-modules with elliptic sheaves.   The Arithmetic of Function Fields and Related Topics On v-adic periods of t-motives Yuichiro Taguchi (Kyushu University) 2011-08-17   I will give an exposition of Mishiba's results on the equality between the transcendental degree of the field generated by the v-adic periods of a t-motive M and the dimension of the Tannakian Galois group for M,where v is a   The Arithmetic of Function Fields and Related Topics A basis for the space of weakly holomorphic Drinfeld modular forms Choi, Soyoung (Dongguk University) 2011-08-16   We construct a natural basis for the space of weakly holomorphic Drinfeld modular forms and observe some arithmetic properties of coefficients of the basis elements. In precise we find that the basis elements satisfy a generating function and find the duality between coefficients of the basis elements. Moreover we obtain congruence properties of $t$-expansion coefficients of these functions.   The Arithmetic of Function Fields and Related Topics A Determinant formula for congruent zeta functions of abelian function fields Ahn, Jaehyun (Chungnam National University) 2011-08-16   we give a determinant formula for congruent zeta functions of abelian function fi elds. We also give some examples of congruent zeta functions when the conductor of abelian function field is prime.   The Arithmetic of Function Fields and Related Topics Coefficients and Hecke eigenvalues of Drinfeld modular forms Cecile Armana (Max-Planck-Institut) 2011-08-16   Drinfeld modular forms are analogs over the function field $\mathbf{F}_{q}(T)$ of classical modular forms. Unlike the classical situation, the action of Hecke operators on the analytical expansion of such modular forms is not well understood. In this talk, I will present formulas giving certain coefficients in terms of Hecke eigenvalues, and vice versa, and discuss some applications. The main tool for the proof is an estimate for power sums of coefficients of the Carlitz module.   The Arithmetic of Function Fields and Related Topics Mock theta functions via Ramanujan's reciprocity theorem Kang, Soonyi (KAIST) 2011-08-16   In earlier work, we showed that two mock Jacobi forms add to a Jacobi theta function using Ramanujan's three variable reciprocity theorem.  In this talk, we revisit the reciprocity theorems to study its further relation with mock theta functions.   The Arithmetic of Function Fields and Related Topics Odd divisor functions formula derived from Weierstrass p-function. Kim, Daeyeol (NIMS) 2011-08-16   In this talk, I will explain basic properties of hypergeometric series and elliptic functions.And then we shall prove new  convolution relations for divisor functions derived from Weierstrass p-functions and basic hypergeometric series.   The Arithmetic of Function Fields and Related Topics On a Goldbach-type question in F_q[t] Andreas Bender (POSTECH) 2011-08-16   The Goldbach conjecture asserts that every even integer greater than two is the sum of two primes. An analogous conjecture can be formulated in the ring of monic polynomials in one variable over a finite field. This talk is about an approach to this conjecture involving prime values of polynomials and a tool which is available only in the polynomial case. The techniques involve some explicit geometry of plane curves over finite fields and an interplay with the corresponding function field extensions, including the Cebotarev density theorem.   The Arithmetic of Function Fields and Related Topics On Goss problem concerning the derivative modulo p of certain Artin L functions Bruno Angles (Universite de Caen) 2011-08-16   We will consider a problem formulated by David Goss concerning the derivative modulo $p$ of certain Artin L-functions associated to cyclotomic function fields in characteristic $p.$ We will give a positive answer for a weak version of this problem. Our approach will be similar to Iwasawa's construction of Kubota- Leopoldt $p$-adic L-functions.   The Arithmetic of Function Fields and Related Topics Representations of integers by $x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4$ Eum, Icksun (KAIST) 2011-08-16   et $r_Q(n)$ be the representation number of a nonnegative integer $n$ by the quaternary quadratic form $Q=x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4$. We prove the identity $r_Q(1)r_Q(p^2n)=r_Q(p^2)r_Q(n)$ for any prime $p$ different from $13$ and any positive integer $n$ prime to $p$. And, we explicitly determine $r_Q(n^2)$ for any integer $n$, too.

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