June Number Theory Days
June 5 @ 1:00 pm – 3:00 pm
Abstract
We wish to present a recent work done with Sébastien Darses and Berend Ringeling. We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties—including Eisenstein series and period functions—that were originally introduced and studied by Lewis and Zagier, and later by Bettin and Conrey in the case of the Riemann zeta function, and more recently by Lewis and Zagier for odd real characters. These tools yield closed-form expressions for the moments of a measure defined via a weighted mean square of the L-function. These moments not only provide a complete characterization of the modulus of the L-function on the critical line, but also imply an infinite number of non-trivial positivity conditions valid for all primitive characters, real or not.
