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Equidistribution of the Fourier coefficients of Hecke cusp forms and applications

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Speaker: 
Oleksiy Klurman
Affiliation: 
University of Bristol/MPIM
Date: 
Wed, 2021-04-28 14:30 - 15:30
Parent event: 
Number theory lunch seminar

I will discuss joint work with A. Mangerel, where we establish a general
joint equidistribution result for the Fourier coefficients of Hecke cusp
forms. One simple to state consequence of such a result is that the set of
integers with, say, $\tau(n+2)<\tau(n+1)<\tau(n)$ where $\tau$ is
the Ramanujan $\tau$-function, has a positive upper density
(previously, even the infinitude of such a set was unknown).

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