Ergodic Theory Seminar - Tariq Osman

Tariq Osman
Brandeis University

Title
Limit Theorems for Siegel Theta Series

Abstract
Given a quadratic form, Q, in k variables, and fixed weight function, f, we define its associated Siegel theta series as:
S^Q_N(t) := \sum_{n \in \Z^k} f(N^{-1} n) e^{\pi i Q(n) t},
where t is a real number in the interval [0,1]. Such sums have found application in various problems from number theory to mathematical physics.
We discuss how dynamical methods can be used to prove the existence of the limit distribution for appropriately normalized theta series in the case when Q is a generic quadratic form, and f is a Schwartz function. This is part of work in progress with J. Griffin and J. Marklof.

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