TY - JOUR

T1 - On the number of sign changes of hecke eigenvalues of newforms

AU - Kohnen, Winfried

AU - Lau, Yuk K.

AU - Shparlinski, Igor E.

N1 - Copyright 2008 Cambridge University Press. Article originally published in Journal of the Australian Mathematical Society, Vol. 85, Iss. 1, pp. 87-94. The original article can be found at http://dx.doi.org/10.1017/S1446788708000323

PY - 2008/8

Y1 - 2008/8

N2 - We show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k,N)x/log17x positive and negative coefficients a(n) with n ≤ x in the Fourier expansion of any non-zero cuspidal Hecke eigenform of even integral weight k ≥ 2 and squarefree level N that is a newform, where C(k,N) depends only on k and N. From this we deduce the existence of a sign change in a short interval.

AB - We show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k,N)x/log17x positive and negative coefficients a(n) with n ≤ x in the Fourier expansion of any non-zero cuspidal Hecke eigenform of even integral weight k ≥ 2 and squarefree level N that is a newform, where C(k,N) depends only on k and N. From this we deduce the existence of a sign change in a short interval.

UR - http://www.scopus.com/inward/record.url?scp=56749161103&partnerID=8YFLogxK

U2 - 10.1017/S1446788708000323

DO - 10.1017/S1446788708000323

M3 - Article

AN - SCOPUS:56749161103

VL - 85

SP - 87

EP - 94

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 1

ER -