Displaying similar documents to “Real zeros of holomorphic Hecke cusp forms”

Real zeros of holomorphic Hecke cusp forms and sieving short intervals

Kaisa Matomäki (2016)

Journal of the European Mathematical Society

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We study so-called real zeros of holomorphic Hecke cusp forms, that is, zeros on three geodesic segments on which the cusp form (or a multiple of it) takes real values. Ghosh and Sarnak, who were the first to study this problem, showed the existence of many such zeros if many short intervals contain numbers whose prime factors all belong to a certain subset of the primes.We prove new results concerning this sieving problem which leads to improved lower bounds for the number of real zeros. ...

A local large sieve inequality for cusp forms

Jonathan Wing Chung Lam (2014)

Journal de Théorie des Nombres de Bordeaux

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We prove a large sieve type inequality for Maass forms and holomorphic cusp forms with level greater or equal to one and of integral or half-integral weight in short interval.