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

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

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