Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two (with an appendix)

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 & Saha in the appendix.
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Submitted on : Thursday, February 25, 2016 - 11:37:58 AM
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E Kowalski, A Saha, Emmanuel Royer, Jyoti Sengupta, Jie Wu. Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two (with an appendix). Ramanujan Journal (The), 2016, 39, pp.179-199. ⟨hal-01278962⟩

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