Explicit inner product formulas and Bessel period formulas for HST lifts

DOI10.1215/21562261-2022-0004arXiv1810.02603WikidataQ113751493 ScholiaQ113751493MaRDI QIDQ6307748

Publication date: 5 October 2018

Abstract: We explicitly give an inner product formula and a Bessel period formula for theta series on GSp(4), which was studied by Harris, Soudry and Taylor. As a consequence, we prove a non-vanishing of the theta series of small weights and we give a criterion for the non-vanishing of the theta series modulo a prime.

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Theta series; Weil representation; theta correspondences (11F27) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Iwasawa theory (11R23) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

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