#### Boğaziçi University Mathematics Colloquium

The Voronoi formula and double Dirichlet series
E. Mehmet Kıral
Texas A&M University, United States of America
Özet : A Voronoi formula is an identity where on one side, there is a weighted sum of Fourier coefficients of an automorphic form twisted by additive characters, and on the other side one has a dual sum where the twist is perhaps by more complicated exponential sums. It is a very versatile tool in analytic studies of L-functions. In joint work with Fan Zhou we come up with a proof of the identity for L-functions of degree N. The proof involves an identity of a double Dirichlet series which in turn yields the desired equality for a single Dirichlet coefficient. The proof is robust and applies to L-functions which are not yet proven to come from automorphic forms, such as Rankin-Selberg L-functions. The first two thirds of my talk should be accessible to a general audience.
 Tarih : 30.12.2015 Saat : 14:00 Yer : TB 250 Dil : English