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  The Fourier coefficients of Eisenstein series newforms

Linowitz, B., & Thompson, L. (2019). The Fourier coefficients of Eisenstein series newforms. In Automorphic forms and related topics (pp. 169-176). Providence, RI: American Mathematical Society.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-69B4-B Version Permalink: https://hdl.handle.net/21.11116/0000-0007-A878-5
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... the Author may post the peer-reviewed manuscript of the Work on the Author’s own website, contribute it to the Author’s institutional repository, and post it on arXiv.org, all provided that no commercial use and no derivative works are permitted. http://www.ams.org/arc/ctp/ctp-form.pdf am 11.01.2021
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https://doi.org/10.1090/conm/732/14788 (Publisher version)
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 Creators:
Linowitz, Benjamin, Author
Thompson, Lola1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: In this article, we study the Fourier coefficients of Eisenstein series newforms. We obtain a sharp refinement of the strong multiplicity-one theorem by showing that the density of primes p for which the pth Hecke eigenvalues of two distinct Eisenstein series newforms differ is of the form 1/n for some n ≥ 2. Additionally, we show that if f is an Eisenstein series newform whose Fourier coefficients af (n) are real then there is a constant δ > 0 such that the
sequence (af (n))n≤x has at least δx sign changes.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 8
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1090/conm/732/14788
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Title: Building Bridges: 3rd EU/US Summer School and Workshop, Automorphic Forms and Related Topics
Place of Event: Sarajevo
Start-/End Date: 2016-07-11 - 2016-07-22

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Title: Automorphic forms and related topics
Source Genre: Proceedings
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Publ. Info: Providence, RI : American Mathematical Society
Pages: 298 Volume / Issue: - Sequence Number: - Start / End Page: 169 - 176 Identifier: DOI: 10.1090/conm/732
ISBN: 978-1-4704-3525-7

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Title: Contemporary Mathematics
Source Genre: Series
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Pages: - Volume / Issue: 732 Sequence Number: - Start / End Page: - Identifier: -