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Averages of central \(L\)-values of Hilbert modular forms with an application to subconvexity. (English) Zbl 1241.11057

Summary: We use the relative trace formula to obtain exact formulas for central values of certain twisted quadratic base change \(L\)-functions averaged over Hilbert modular forms of a fixed weight and level. We apply these formulas to the subconvexity problem for these \(L\)-functions. We also establish an equidistribution result for the Hecke eigenvalues weighted by these \(L\)-values

MSC:

11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F72 Spectral theory; trace formulas (e.g., that of Selberg)
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References:

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