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Additive bases with coefficients of newforms

  • Victor Cuauhtemoc García and Florin Nicolae EMAIL logo
Published/Copyright: January 16, 2018

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.

MSC 2010: 11F30 11P05

Communicated by Jan Bruinier


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Received: 2017-04-22
Revised: 2017-11-15
Published Online: 2018-01-16
Published in Print: 2018-09-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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