Poisson Statistics and the Value Distribution of the Epstein Zeta Function

Joint IAS-PU Number Theory Seminar
Topic:Poisson Statistics and the Value Distribution of the Epstein Zeta Function
Speaker:Anders Sodergren
Affiliation:Member, School of Mathematics
Date:Thursday, January 19
Time/Room:4:30pm - 5:30pm/S-101

We will discuss the value distribution of the Epstein zeta function E_n(L,cn) for real c and a random lattice L of covolume 1 and large dimension n. Important ingredients in our study will be the distribution of vector lengths in a random lattice as the dimension n tends to infinity and a new bound on the remainder term in the generalized circle problem. We will also present some applications of our results to for example the distribution of heights of flat tori.