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Zbl 1131.11340
Habsieger, Laurent; Royer, Emmanuel
$L$-functions of automorphic forms and combinatorics: Dyck paths. (English)
[J] Ann. Inst. Fourier 54, No. 7, 2105-2141 (2004). ISSN 0373-0956; ISSN 1777-5310/e

Summary: We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the $L$-functions of modular forms of $\text{GL}(2)$ and $\text{GL}(3)$. We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.

MSC 2000:: *11F67 Special values of automorphic L-series, etc
05A16 Asymptotic enumeration
05A19 Combinatorial identities
11B75 Combinatorial number theory
11F11 Modular forms, one variable

Keywords: symmetric square; modular form; $L$-function; Dyck path; combinatorics; Narayana number

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