NDLI: Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two : With an appendix by E. Kowalski and A. Saha

Content Provider	Springer Nature Link
Author	Sengupta, Jyoti Wu, Jie Royer, Emmanuel
Copyright Year	2015
Abstract	In this paper, we show that half of non-zero coefficients of the spinor zeta function of a Siegel cusp form of genus 2 are positive and half are negative. We also prove results concerning the non-vanishing in short intervals and strong cancellation among the coefficients evaluated at powers of a fixed prime. Our results rest on a Serre’s type density result established by Kowalski and Saha in the Appendix.
Ending Page	199
Page Count	21
Starting Page	179
File Format	PDF
ISSN	13824090
e-ISSN	15729303
Journal	The Ramanujan Journal
Issue Number	1
Volume Number	39
Language	English
Publisher	Springer US
Publisher Date	2015-01-22
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Other Dirichlet series and zeta functions Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms Functions of a Complex Variable Field Theory and Polynomials Asymptotic results on arithmetic functions Fourier coefficients Fourier coefficients of automorphic forms Fourier Analysis Siegel form Spinor zeta function Rate of growth of arithmetic functions Number Theory Hecke eigenvalues Combinatorics
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two : With an appendix by E. Kowalski and A. Saha