Colloquium abstracts

A. Raghuram
Oklahoma State University, USA
July 28, 2011

From Calculus to Number Theory: An introduction to the special values of L-functions:  An L-function is a function of one complex variable that is attached to some interesting arithmetic or geometric data. The values of such an L-function, at interesting points, give structural information about the data to which it is attached. This talk will be an introduction, via examples, to the subject of special values of L-functions. I will begin by recalling some classical formulae which one usually encounters in an advanced course in Calculus. These formulae, when recast in modern language, are the prototypes of special values of L-functions. Starting at an elementary level, I will build up toward classical results of Manin and Shimura on the L-functions of modular forms or of automorphic forms on GL(2); but I will present the results in a fashion which admits generalizations to higher GL(n).