Real zeros of holomorphic Hecke cusp forms and sieving short intervals

Kaisa Matomäki

Journal of the European Mathematical Society (2016)

  • Volume: 018, Issue: 1, page 123-146
  • ISSN: 1435-9855

Abstract

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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.

How to cite

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Matomäki, Kaisa. "Real zeros of holomorphic Hecke cusp forms and sieving short intervals." Journal of the European Mathematical Society 018.1 (2016): 123-146. <http://eudml.org/doc/277197>.

@article{Matomäki2016,
abstract = {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.},
author = {Matomäki, Kaisa},
journal = {Journal of the European Mathematical Society},
keywords = {cusp forms; real zeros; sieving short intervals; cusp forms; real zeros; sieving short intervals},
language = {eng},
number = {1},
pages = {123-146},
publisher = {European Mathematical Society Publishing House},
title = {Real zeros of holomorphic Hecke cusp forms and sieving short intervals},
url = {http://eudml.org/doc/277197},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Matomäki, Kaisa
TI - Real zeros of holomorphic Hecke cusp forms and sieving short intervals
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 1
SP - 123
EP - 146
AB - 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.
LA - eng
KW - cusp forms; real zeros; sieving short intervals; cusp forms; real zeros; sieving short intervals
UR - http://eudml.org/doc/277197
ER -

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