Department of Mathematics,
University of California San Diego
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Math 211B - Group Actions Seminar
Matthew Welsh
University of Bristol
Bounds for theta sums in higher rank
Abstract:
In joint work with Jens Marklof, we prove new upper bounds for theta sums -- finite exponential sums with a quadratic form in the oscillatory phase -- in the case of smooth and box truncations. This generalizes results of Fiedler, Jurkat and Körner (1977) and Fedotov and Klopp (2012) for one-variable theta sums and, in the multi-variable case, improves previous estimates obtained by Cosentino and Flaminio (2015). Key inputs in our approach include the geometry of $\mathrm{Sp}(n, \mathbb{Z}) \backslash \mathrm{Sp}(n, \mathbb{R})$, the automorphic representation of theta functions and their growth in the cusp, and the action of the diagonal subgroup of $\mathrm{Sp}(n, \mathbb{R})$.
Host: Brandon Seward
May 5, 2022
10:00 AM
AP&M 6402
Zoom ID 967 4109 3409
Email an organizer for the password
Research Areas
Ergodic Theory and Dynamical Systems****************************
