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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 30, Issue 5

Issues

Additive bases with coefficients of newforms

Victor Cuauhtemoc García
  • Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana – Azcapotzalco, C.P. 02200, Mexico City, Mexico
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/ Florin Nicolae
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  • Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
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Published Online: 2018-01-16 | DOI: https://doi.org/10.1515/forum-2017-0091

Abstract

Let f(z)=n=1a(n)e2πinz be a normalized Hecke eigenform in S2knew(Γ0(N)) with integer Fourier coefficients. We prove that there exists a constant C(f)>0 such that any integer is a sum of at most C(f) coefficients a(n). We have C(f)ε,kN6k-316+ε.

Keywords: Newform; Fourier coefficients; additive basis

MSC 2010: 11F30 11P05

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About the article


Received: 2017-04-22

Revised: 2017-11-15

Published Online: 2018-01-16

Published in Print: 2018-09-01


Citation Information: Forum Mathematicum, Volume 30, Issue 5, Pages 1079–1087, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0091.

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