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Quantitative Joint Equidistribution of Transformed Hecke Eigenvalues and Frobenius Traces
Algebraic Geometry and Number Theory| Speaker: | Tian Wang, MPIM Bonn |
| Related Webpage: | https://sites.google.com/uic.edu/twang/home |
| Location: | 2112 MSB |
| Start time: | Thu, Oct 29 2026, 11:00AM |
Description
In 1968, Birch proved that normalized Frobenius traces of elliptic curves over finite fields, averaged over families of curves, are equidistributed with respect to the Sato-Tate measure. Analogous results for normalized Hecke eigenvalues, with respect to the p-adic Plancherel measure, were obtained by Sarnak (1987) for Maass forms and by Serre (1997) for holomorphic modular forms. These classical theorems motivate finer quantitative questions about the arithmetic of modular forms and elliptic curves. In this talk, I will show how analytic techniques yield quantitative equidistribution results for transformations of normalized Hecke eigenvalues and Frobenius traces. I will show how these transformations change the limiting distributions and how this is reflected in the rate of convergence. This is joint work with Mohammad Hamdar.