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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.

MSC:
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
Citations:
Zbl 1295.11087
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References:
[1] doi:10.1016/j.aim.2014.03.020 · Zbl 1295.11087
[2] doi:10.1155/S1073792898000476 · Zbl 0920.11060
[3] doi:10.1215/S0012-7094-01-10737-0 · Zbl 1006.11048
[4] doi:10.1112/S0024611504015175 · Zbl 1075.11058
[5] doi:10.1007/s00039-012-0191-6 · Zbl 1270.11082
[6] doi:10.1023/B:COMP.0000018137.38458.68 · Zbl 1053.11071
[7] doi:10.1007/s00013-011-0334-2 · Zbl 1312.11036
[8] doi:10.1017/CBO9780511526091.015
[9] doi:10.1112/S0010437X07002679 · Zbl 1149.11023
[10] ; Katz, Random matrices, Frobenius eigenvalues, and monodromy. American Mathematical Society Colloquium Publications, 45, (1999) · Zbl 0958.11004
[11] doi:10.1007/s002200000261 · Zbl 1051.11048
[12] doi:10.1073/pnas.0501723102 · Zbl 1159.11317
[13] doi:10.4007/annals.2009.170.981 · Zbl 1251.11058
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