Abstract

In 1997 Sinha introduced a class of Anderson t-modules with complex multiplication by rings of integers in Carlitz cyclotomic extensions. Using Anderson's theory of solitons and Coleman functions, he showed that the coordinates of periods of these t-modules could be expressed in terms of values of Thakur's geometric Gamma function at rational arguments. As part of these constructions, Anderson and Sinha also defined algebraic Hecke characters whose infinity types are related to the CM-type of the t-module. We show that the Goss L-series for Sinha modules are products of these Hecke L-series, and moreover, we show that their special values at s=0 are expressible in terms of function field Gamma values. Joint with E. Davis.

 

Organizer: Chieh-Yu Chang (NTHU)