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Speaker:

Noam Kimmel
Affiliation:

Tel-Aviv University
Date:

Wed, 23/10/2024 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar We explore the zeros of certain Poincaréseries P(k,m) of weight k and index m for the full modular group. These are distinguished modular forms, which have played a key role in the analytic theory of modular forms. We study the zeros of P(k,m) when the weight k tends to infinity. The case where the index m is constant was considered by Rankin who showed that in this case almost all of the zeros lie on the unit arc `|z|`

=1. In this talk we will explore the location of the zeros when the index m grows with the weight k, finding a range of different limit laws. Along the way, we also establish a version of Quantum Unique Ergodicity for some ranges.

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