Pellarin L-series for Drinfeld modules on elliptic curves

04/05/2018 - 12:15pm
04/05/2018 - 1:10pm
Matt Papanikolas (Texas A&M University)

In 2012 Pellarin defined a new class of L-series over the polynomial ring over a finite field that take values in the Tate algebra of the closed unit disk for the place at infinity. These L-series interpolate both special values of Dirichlet L-functions as well as other special values of Goss L-series related to the Carlitz module. Subsequent multivariable versions were studied by Anglès, Pellarin, and Tavares Ribeiro, with applications to analogues of Stark units. In this talk we will discuss approaches to Pellarin's theory over more general rings, in particular over coordinate rings of elliptic curves over finite fields. Using the theory of shtuka functions, we prove special value formulas for Pellarin L-series that take values in the affinoid algebra of the elliptic curve. Joint with N. Green.

Millikan 2099, Pomona College

Claremont Graduate University | Claremont McKenna | Harvey Mudd | Pitzer | Pomona | Scripps
Proudly Serving Math Community at the Claremont Colleges Since 2007
Copyright © 2018 Claremont Center for the Mathematical Sciences