Some numerical computations concerning spinor zeta functions in genus 2 at the central point. (English) Zbl 1076.11030
Summary: We numerically compute the central critical values of odd quadratic character twists with respect to some small discriminants \(D\) of spinor zeta functions attached to Siegel-Hecke eigenforms \(F\) of genus 2 in the first few cases where \(F\) does not belong to the Maass space. As a result, in the cases considered we can numerically confirm a conjecture of S. Böcherer [Bemerkungen über die Dirichletreihen von Koecher und Maass. Math. Gottingensis, Schriftenr. Sonderforschungsbereichs Geom. Anal. 68 (1986)], according to which these central critical values should be proportional to the squares of certain finite sums of Fourier coefficients of \(F\).
MSC:
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 11F30 | Fourier coefficients of automorphic forms |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11Y35 | Analytic computations |
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