Bounds for Theta sums

Vortrag von Dr. Tariq Osman

Datum: 16.10.25  Zeit: 16.05 - 17.05  Raum: ETH HG G 43

A Theta sum is an exponential sum of the form \(S_N (x) := \sum_{n = 1}^N e^{2 \pi i n^2 x}\), where \(x \in [0,1]\). For given \(x\), we may think of \(S_N\) as a path in the complex plane. We discuss how methods from hyperbolic geometry, and dynamical systems can be used to understand how far such a path can take you from the origin, as a function of \(N\).