On the nonnegativity of \(L(\frac12,\pi)\) for \(\text{SO}_{2n+1}\)

zbMath1067.11026arXivmath/0402371MaRDI QIDQ1423981

Stephen Rallis, Erez M. Lapid

Publication date: 8 March 2004

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402371

zbMATH Keywords

partial \(L\)-function\(L\)-function of a cuspidal representationvalues at the critical prints

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

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On the nonvanishing of the central value of the Rankin-Selberg 𝐿-functions ⋮ On the 4-norm of an automorphic form ⋮ Shtukas and the Taylor expansion of \(L\)-functions ⋮ First moment of Rankin-Selberg central \(L\)-values and subconvexity in the level aspect ⋮ Formal degrees and local theta correspondence ⋮ Automorphic period and the central value of Rankin-Selberg L-function ⋮ \(L\)-functions and theta correspondence for classical groups ⋮ Special values of motivic \(L\)-functions and zeta-polynomials for symmetric powers of elliptic curves ⋮ On the residue method for period integrals ⋮ On the fourth moment of Hecke–Maass forms and the random wave conjecture ⋮ Positivity of \(L(\frac 1 2,\pi)\) for symplectic representations

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