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Sign Changes of Cusp Forms and Geodesic Restrictions

Algebraic Geometry and Number Theory

Speaker: Peter Zenz, Stanford
Related Webpage: https://sites.google.com/view/peterzenz/about-me
Location: 2112 MSB
Start time: Wed, Mar 6 2024, 2:10PM

In this talk we review approaches to detect sign changes of Hecke Maass Cusp Form and holomorphic Hecke cusp forms for SL2(Z) on the vertical geodesic connecting 0 and infinity. Sign changes of cusp forms are intimately related to questions about certain moments of L-functions and shifted convolution problems. We highlight differences and similarities between the holomorphic and real analytic case. Finaly, we will explore how to detect a sharp upper bound for the number of sign changes for almost all holomorphic Hecke cusp forms in a compact interval on the vertical geodesic (this is ongoing work).