On the number of sign changes of hecke eigenvalues of newforms

Winfried Kohnen*, Yuk K. Lau, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
19 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)87-94
Number of pages8
JournalJournal of the Australian Mathematical Society
Volume85
Issue number1
DOIs
Publication statusPublished - Aug 2008

Bibliographical note

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

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