On Real Zeros of Holomorphic Hecke Cusp Forms and Sieving Short Intervals

Joint IAS-PU Number Theory Seminar
Topic:On Real Zeros of Holomorphic Hecke Cusp Forms and Sieving Short Intervals
Speaker:Kaisa Matomäki
Affiliation:University of Turku, Finland
Date:Thursday, October 13
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/joint/matomaki

A. Ghosh and P. Sarnak have recently initiated the study of so-called real zeros of holomorphic Hecke cusp forms, that is zeros on certain geodesic segments on which the cusp form (or a multiple of it) takes real values. In the talk I'll first introduce the problem and outline their argument that many such zeros exist if many short intervals contain numbers whose all prime factors belong to a certain subset of primes. Then I'll speak about new results on this sieving problem which lead to improved lower bounds for the number of real zeros.