Axiomatic Multiple Dirichlet Series, Moments of L-Functions, and Symmetry

Event Date
2025-02-19
Event Time
02:30 pm ~ 04:00 pm
Event Location
Temple University, Wachman Hall 412

Ian Whitehead, Swarthmore College

Abstract: I will discuss joint work in progress with Will Sawin on function field multiple Dirichlet series constructed based on a set of axioms from algebraic geometry. These series have applications to moments of Dirichlet L-functions for characters of fixed order. We prove functional equations that imply meromorphic continuation for many of these series. The most striking feature of our work is a set of detailed predictions for the symmetries involved in any given moment computation. We find a complete tabulation of moments that are possible to compute via known multiple Dirichlet series methods, including several new moments.