A1 Refereed original research article in a scientific journal

On Short Sums Involving Fourier Coefficients of Maass Forms



Authors: Jääsaari J

Publisher: UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX

Publication year: 2020

Journal: Journal De Theorie Des Nombres De Bordeaux

Journal name in source: JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX

Journal acronym: J THEOR NOMBR BORDX

Volume: 32

Issue: 3

First page : 761

Last page: 793

Number of pages: 33

ISSN: 1246-7405

eISSN: 2118-8572

DOI: https://doi.org/10.5802/jtnb.1142

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/52258876


Abstract
We study sums of Hecke eigenvalues of Hecke-Maass cusp forms for the group SL(n, Z), with general n >= 3, over short intervals of certain length under the assumption of the generalised Lindelof hypothesis and a slightly stronger upper bound concerning the exponent towards the Ramanujan-Petersson conjecture than is currently known. In particular, in this case we evaluate the second moment of the sums in question asymptotically.


Keywords:
Fourier coefficients of automorphic forms, higher rank Maass cusp forms, sums of Hecke eigenvalues

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Last updated on 26/11/2024 08:10:26 PM