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

Abstract

© World Scientific Publishing Company. 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 σ the sequence (a(pjn))n0 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.