Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two. With an appendix by E. Kowalski and A. Saha. With an appendix by E. Kowalski and A. Saha. (English) Zbl 1402.11074
Summary: 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.
MSC:
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 11F30 | Fourier coefficients of automorphic forms |
| 11M41 | Other Dirichlet series and zeta functions |
| 11N37 | Asymptotic results on arithmetic functions |
| 11N56 | Rate of growth of arithmetic functions |
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