Sign changes of Fourier coefficients of cusp forms supported on prime power indices-Reference-Cited by-同舟云学术

Sign changes of Fourier coefficients of cusp forms supported on prime power indices

Published:2014-10-29 Issue:08 Volume:10 Page:1921-1927
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Kohnen Winfried¹,Martin Yves²

Affiliation:

1. Mathematisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany

2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

Abstract

Let f be an even integral weight, normalized, cuspidal Hecke eigenform over SL2(ℤ) with Fourier coefficients a(n). Let j be a positive integer. We prove that for almost all primes p the sequence (a(pjn))n≥0 has infinitely many sign changes. We also obtain a similar result for any cusp form with real Fourier coefficients that provide the characteristic polynomial of some generalized Hecke operator is irreducible over ℚ.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042114500626

Reference7 articles.

1. Irreducibility of Hecke polynomials

2. The irreducibility of some level 1 Hecke polynomials

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4. On an open problem of Sankaranarayanan

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