Steven Sperber : L-functions associated with families of exponential sums

Posted by Emily Dumas , part of the Departmental Colloquium.

At

Feb. 25, 2011, 3 p.m.

In

SEO 636

Abstract

Given a family of varieties defined over a finite field of characteristic p or a family of exponential sums we consider for each fiber the set of reciprocal zeros and poles for the zeta function or L-function. We construct new L-functions from this collection of algebraic numbers by taking a product (over the fibers) of factors that have the symmetric powers (or tensor powers, or exterior powers) of the numbers (or a subset of them) in our set as reciprocal zeros. In a joint work with Haessig, we study these L-functions for a general family of non-degenerate toric exponential sums and obtain bounds for the degree of the L-function and a rudimentary estimate for the p-divisibility of the reciprocal zeros and poles of these L-functions.