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
SN - 1446-7887
VL - 85
SP - 87
EP - 94
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 1
ER -