











Title 


Speaker 
Charles M. Newman



Date 
20181114 


Host 



Place 
KAIST 




Abstract : One fairly standard version of the Riemann Hypothesis (RH) is that a specific probability density on the real line has a moment generating function (Laplace transform) that, as an analytic function on the complex plane, has all its zeros pure imaginary. We'll review a series of results that span the period from the 1920's to 2018 concerning a perturbed version of the RH. In that perturbed version, due to Polya, the log of the probability density is modified by a quadratic term.
This gives rise to an implicitly defined real constant known as the de BruijnNewman Constant, Lambda. The conjecture and now theorem (Newman 1976, Rodgers and Tao 2018) that Lambda is greater than or equal to zero is complementary to the RH which is equivalent to Lambda less than or equal to zero; The conjecture/theorem is a version of the dictum that the RH, if true, is only barely so. Until very recently, the best upper bound, was a 2009 result of Ki, Kim and Lee that Lambda is strictly less than 1/2. 





