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The sixth moment of automorphic \(L\)-functions. (English) Zbl 06722476
Summary: We consider the \(L\)-functions \(L(s,f)\), where \(f\) is an eigenform for the congruence subgroup \(\Gamma_1(q)\). We prove an asymptotic formula for the sixth moment of this family of automorphic \(L\)-functions.

11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11M41 Other Dirichlet series and zeta functions
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
Zbl 1295.11087
Full Text: DOI
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