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Non-vanishing of Hilbert Poincaré series. (English) Zbl 1422.11108

Summary: We prove some non-vanishing results of Hilbert Poincaré series. We derive these results, by showing that the Fourier coefficients of Hilbert Poincaré series satisfy some nice orthogonality relations for sufficiently large weight as well as for sufficiently large level. To prove later results, we generalize a method of E. Kowalski et al. [Mathematika 57, No. 1, 31–40 (2011; Zbl 1220.11063)].

MSC:

11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
40A05 Convergence and divergence of series and sequences

Citations:

Zbl 1220.11063
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References:

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