Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Calin Adrian Diaconu
Affiliation:

U of Minnesota/MPI
Date:

Wed, 16/02/2011 - 14:15 - 15:15 Multiple Dirichlet series (MDS) are Dirichlet series in several complex variables mainly used in studying various analytic properties within certain families of automorphic L-functions (e.g., the family of all quadratic twists of a fixed L-function). I will begin by discussing the main motivation for studying these objects, with particular focus on the MDS associated to moments of quadratic Dirichlet L-functions. We have a local-global compatibility, and when the MDS are associated to moments of quadratic L-series, their local components are determined by connecting moments of character sums of hyperelliptic curves of a given genus over finite fields to traces on spaces of automorphic forms - a comparison of Arthur-Selberg and Grothendieck-Lefschetz trace formulas. In particular, I will present a tight connection with the recent work of J. Bergstr\"om, C. Faber and G. van der Geer. (Joint work with V. Pasol)

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246