Document Zbl 07810348

Wide moments of L-functions. I: Twists by class group characters of imaginary quadratic fields. (English) Zbl 07810348

Algebra Number Theory 18, No. 4, 735-770 (2024).

Let \(\pi\) be a cuspidal automorphic representation of \(\mathrm{GL}_2\) over \(\mathbb{Q}\) and let \(\Omega\) be a Hecke character (of conductor 1) of an imaginary quadratic field \(K\). The main purpose of this paper is to compute certain “wide moments” of central values of Rankin-Selberg \(L\)-functions \(L\bigl(\pi\otimes \Omega,\frac12\bigr)\). As consequence, the nonvanishing of certain automorphic periods, which combined with the moment calculation, yields weak simultaneous nonvanishing result.

Reviewer: Sami Omar (Sukhair)

Cited in 1 Document

MSC:

11F67	Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11M41	Other Dirichlet series and zeta functions

Keywords:

moments of \(L\)-functions; periods of automorphic forms

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