##### 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****************************