Spectral average of central values of automorphic \(L\)-functions for holomorphic cusp forms on \(\mathrm{SO}_0(m,2)\). I

DOI10.1016/j.jnt.2012.04.020zbMath1282.11052arXiv1906.01172OpenAlexW2007956847MaRDI QIDQ452377

Masao Tsuzuki

Publication date: 21 September 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.01172

zbMATH Keywords

Poincaré seriesAutomorphic L-functions of orthogonal groupsSpectral expansions

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Cites Work

• Shintani function and its application to automorphic \(L\)-functions for classical groups. I: The case of orthogonal groups
• Generalized Whittaker vectors for holomorphic and quaternionic representations
• The expressions of the Harish-Chandra \(C\)-functions of semisimple Lie groups \(\text{Spin}(n,1)\), \(\text{SU}(n,1)\)
• Spherical Functions for the Semisimple Symmetric Pair (Sp(2, ℝ), SL(2, ℂ))
• On standard L-functions attached to automorphic forms on definite orthogonal groups
• On Dirichlet series whose coefficients are class numbers of integral binary cubic forms
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