Article Dans Une Revue The Ramanujan Journal Année : 2016

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

Résumé

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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hal-01278962 , version 1 (25-02-2016)

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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). The Ramanujan Journal, 2016, 39, pp.179-199. ⟨10.1007/s11139-014-9667-3⟩. ⟨hal-01278962⟩
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