The values of Riemann's zeta function at even positive integers as well as at negative integers first computed by Euler, with the double appearance of Bernoulli numbers and the occurrence of the number pi, suggest the structure of the functional equation of this function. In the arithmetic of function fields of positive characteristic we have at our disposal, especially after the work of Carlitz and Goss, some variants of Dirichlet series having surprising similarities with Riemann's zeta values at integers and a large spectrum of phenomena reminding of Euler's first observations. In spite of this, no analogue of the functional equation of Riemann's zeta can be even guessed. The aim of this talk is to provide some new evidences that such functional equations must exist and some hint on the shape the Gamma factors should have.
Donnerstag, den 26. Januar 2012 um 17 c.t. Uhr, in INF 288, HS2 Donnerstag, den 26. Januar 2012 at 17 c.t., in INF 288, HS2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Böckle