Algebra & Number Theory

The sixth moment of automorphic $L$-functions

Vorrapan Chandee and Xiannan Li

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We consider the L-functions L(s,f), where f is an eigenform for the congruence subgroup Γ1(q). We prove an asymptotic formula for the sixth moment of this family of automorphic L-functions.

Article information

Algebra Number Theory, Volume 11, Number 3 (2017), 583-633.

Received: 16 February 2016
Revised: 25 July 2016
Accepted: 16 December 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Secondary: 11F11: Holomorphic modular forms of integral weight 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

moment of $L$-functions automorphic $L$-functions $\Gamma_1(q)$


Chandee, Vorrapan; Li, Xiannan. The sixth moment of automorphic $L$-functions. Algebra Number Theory 11 (2017), no. 3, 583--633. doi:10.2140/ant.2017.11.583.

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