Linear Relations of Siegel Poincaré Series and Non-vanishing of the Central Values of Spinor $L$-functions

Wei, Zhining

Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 3, pp. 755-766.

Dans cet article, nous étudions d’abord les relations linéaires des familles à un paramètre des séries de Siegel–Poincaré. Nous donnons ensuite des applications de nos résultats à la non-annulation des coefficients de Fourier des formes propres cuspidales de Siegel et des valeurs centrales.

In this paper, we will first investigate the linear relations of a one parameter family of Siegel Poincaré series. Then we give the applications to the non-vanishing of Fourier coefficients of Siegel cusp eigenforms and the central values.

Classification : 11F46, 11F30, 11F67
Mots clés : Siegel Poincaré series, Fourier coefficients of Siegel cusp forms, non-vanishing of central values, Böcherer conjecture.

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