Title   name Lastest   |   Most hits   년도선택 최근 50건20192018201720162015201420132012201120102009200820072006200520042003200220012000     East Asia Number Theory Conference An analogue of the discriminant function for congruence subgroup and its application to the extremal quasimodular forms Hiroyuki Tsutsumi (Osaka Univ of Health and Sport Sciences) 2008-01-23     East Asia Number Theory Conference Calculation of $l$-adic local Fourier transformations Lei Fu (Nankai Univ.) 2008-01-23      East Asia Number Theory Conference Extended Gauss AGM and isogenous formulas of modular forms Hironori Shiga (Chiba Univ.) 2008-01-23     East Asia Number Theory Conference Modular units and divisor class groups of the modular curves $X_1(N)$ Yifan Yang (National Chiao-Tung Univ.) 2008-01-23      East Asia Number Theory Conference On the Implementation of Tate Pairings Soonhak Kwon (성균관대) 2008-01-23      East Asia Number Theory Conference On the p-adic L-functions for modular forms Masataka Chida (Tohoku Univ.) 2008-01-23     East Asia Number Theory Conference Prime Solutions to Quadratic Fquations Jianya Liu (Shandong Univ.) 2008-01-23      East Asia Number Theory Conference Ramakrishna-Khare Systems in Higher Weights Yih-Jeng YU (National Center for Theoretical Science) 2008-01-23     East Asia Number Theory Conference The first sign change of Fourier coefficients fo cusp forms YoungJu Choie (POSTECH) 2008-01-23     East Asia Number Theory Conference $K_{2i}(O_F)$ for $Z_p$-extension Hourong Qin (Nanjing University) 2008-01-22    Let F be a number field with µp  F if p is odd and µ4  F if p = 2. Let F1/F be the cyclotomicZp-extension, and for all integers n  0, let Fn be the unique intermediate field for F1/F such that[Fn : F] = pn. Let OF be the ring of integers in F and OFn be the integral closure of OF in Fn. ForK2i(OFn){p}, the p-primary subgroup of K2i(OFn), we establish an analogue of the classical Iwasawatheorem. We will discuss the structure of K2i(OFn){p} and study the relation between K2i(OFn){p} andthe p-primary subgroup of the ideal class group of Fn. We will give some equivalent statements for theVandiver conjecture to be true. This is the joint work with Qingzhong Ji.   East Asia Number Theory Conference Congruences between extremal modular forms and theta series of special types modulo powers of 2 and 3 Masao Koike (Kyushu Univ.) 2008-01-22   Heninger, Rains and Sloane proved that the n-th root of the theta series of any extremal even unimodularlattice in Rn have integer coefficients if n is of the form 2i3j5k(i  3).Motivated by their discovery,we find the congruences between extremal modular forms and theta series of special types modulo powersof 2 and 3. This assertion enables us to prove that 2n-th root and 3n-th root of the extremal modularform of weight n2 have at least a non-integer coefficient.   East Asia Number Theory Conference On the coefficients of certain family of modular equations Nam Min Kim (KAIST) 2008-01-22      East Asia Number Theory Conference Regular positive ternary quadratic forms Byeong-Kweon Oh (세종대) 2008-01-22    A positive definite quadratic form f is said to be regular if it globally represents all integers that arerepresented by the genus of f. In 1997, Jagy, Kaplansky and Schiemann provided a list of 913 candidatesof primitive positive definite regular ternary quadratic forms, and all but 22 of them are verified to beregular. In this talk we prove that eight forms among 22 candidates are regular.   East Asia Number Theory Conference The transfer maps for motivic cohomology and Nesternko-Suslin theroem Sung Myung (인하대) 2008-01-22   Transfer Maps for Milnor’s K-theory were first defined by Bass and Tate (1972) for simple extensionsof fields via tame symbol and Weil’s reciprocity law, but their functoriality had not been settled untilKato (1980). Meanwhile, certain motivic cohomology groups, defined in terms of higher Chow groups,are shown to be isomorphic to Milnor’s K-groups of fields by Nesterenko and Suslin (1989). But, in fact,functorial transfer maps for motivic cohomology are easily defined using GW-complex. In this talk, weshow that these natural motivic transfer maps actually agree with the classical but difficult transfer mapsby Bass and Tate. A by-product of this result is another proof of Nesterenko and Suslin’s theorem forthis version of motivic complex.   East Asia Number Theory Conference Tower of the maximal abelian extensions of local fields and their application Xu Fei (Chinese Academy of Sciences) 2008-01-22   The local class field theory gives the explicit description of the maximal abelian extension of a localfield and the corresponding Galois group. From representaion point of view, Langlands has formulatedhis famous local langlands program which extends the local class field theory to general non-abelian cases.This program has recently been proved by Harris and Taylor. In this talk we will study the tower of thesuccessive maximal abelian extensions of local fields and give the explicit description of these fields andthe Galois groups at each level. The main ingredient is to study the algebraic structue of the principalunits in infinite abelian extensions of local fields by using Galois cohomology. As application, we showthere are only finitely many finite covering of given degree of the maximal abelian extension of a local field.   East Asia Number Theory Conference Vahlen's Involution and q-sereis identities Joon Youp Lee (POSTECH) 2008-01-22    After introducing Vahlen’s involution which is a partition bijection, combinatorial proofs of some qseriesidentities will be given. Using this, generalizations will be considered. And derived identities willbe explained in a similar context. Finally, identities in Ramanujan’s lost notebook will be treated.   East Asia Number Theory Conference Truncated Euler Systems Soogil Seo (연세대) 2008-01-21   It is known that the order of the class group ClK of real abelian field K is essentially equal to the orderof the quotient EK/CK of the global units EK by the circular units CK of K. However, the structuresof these two groups are usually very different. Motivated by the theory of circular distributions and thespecial units of Rubin, we introduce a filtration to EK made from the so-called truncated Euler systemsand conjecture that the associated graded module is isomorphic, as a Galois module, to the class group.We use Euler systems to give evidence for this conjecture.   East Asia Number Theory Conference A geometric proof of Mordell's conjecture for function fields Kezheng LI (Capital Normal Univ.) 2008-01-21   Let C, C0 be curves over a base scheme S with g(C)  2. Then the functor T 7! {generically smoothT-morphisms T ×S C0 ! T ×S C} from ((S-schemes)) to ((sets)) is represented by a quasi-finite unramifiedS-scheme. From this one can easily deduce that for any two integers g  2 and g0, there is an integerM(g, g0) such that for any two curves C,C0 over any field k with g(C) = g, g(C0) = g0, there are at mostM(g, g0) separable k-morphisms C0 ! C. This is a today’s strong version of Mordell’s conjecture forfunction fields. From the above method one can also see some interesting properties of higher dimensionalvarieties.   East Asia Number Theory Conference Control Theorems for Abelian Varieties over Global Function Fields Ki-Seng Tan (National Taiwan Univ.) 2008-01-21    We prove the function field analogue for Mazur’s Control theorems for abelian varieties.   East Asia Number Theory Conference On a Local-Global Property of Algebraic Dynamics Liang-Chung Hsia (National Central University) 2008-01-21    A key tool in the study of Diophantine equations is the application of local-global principles, such asthe Hasse principle and the Brauer-Manin obstruction. In this talk, we’ll discuss a question concerninglocal-global principle for algebraic dynamical systems. Let ' : PN ! PN be a morphism of degree d  2defined over a number field K and let P 2 PN(K) be a point with infinite forward orbit O'(P). Let AKdenote the ring of adeles of K and write O'(P) for the closure of O'(P) in PN(AK). Let V  PN be anirreducible variety. Then must it be true that either (i) O'(P) V (K) = O'(P) V (AK) or (ii) thereare positive integers n > m  0 such that 'n(V ) = 'm(V )? We study this question for the dth powermap on P2 and give an affirmative answer for varieties V that are translates of tori in G2m.(This is a joint work with Joseph Silverman.)   East Asia Number Theory Conference On Motivic Transcendence Theory in Positive Characteristic Jing Yu (NCTS, National Tsinghua Univ.) 2008-01-21    I will give a survey of recent progress on t-motives in positive characteristic. In particular the developmentof a motivic Galois theory and its applications to algebraic independence problems. This leadsto the determination of all algebraic relations of sets of transcendental invariants which arise naturallyfrom function field arithmetic.   East Asia Number Theory Conference The non-existence of certain mod 2 Galois representations of some small quadratic fields Yuichiro Taguchi (Kyushu Univ.) 2008-01-21   For some quadratic fields of small discriminant, we prove the non-existence of mod 2 Galois representationsof degree 2 unramified outside 2 and the infinite place. This implies a few special cases of aversion of Serre’s modularity conjecture, of which the original version for the rational number field hasbeen proved recently by Khare and Wintenberger.(This is a joint work with Hyunsuk Moon.)

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