Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions

DOI10.1017/S0305004111000806zbMath1281.11051arXiv1103.5937OpenAlexW3098934836MaRDI QIDQ2883241

Rizwanur Khan

Publication date: 11 May 2012

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.5937

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (9)

Dirichlet \(L\)-functions of quadratic characters of prime conductor at the central point ⋮ Simultaneous non-vanishing of central values of \(\mathrm{GL}(2) \times \mathrm{GL}(3)\) and \(\mathrm{GL}(3)\) \(L\)-functions ⋮ The fourth moment of Dirichlet \(L\)-functions at the central value ⋮ Spectral reciprocity via integral representations ⋮ Non-vanishing of the first derivative of GL(3) ×GL(2) L-functions ⋮ Simultaneous nonvanishing of automorphic \(L\)-functions ⋮ Simultaneous nonvanishing of 𝐺𝐿(2)×𝐺𝐿(2) and 𝐺𝐿(2) 𝐿-functions ⋮ Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke–Maass L-functions in the critical strip ⋮ The second moment of twisted modular \(L\)-functions

Cites Work

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• Hecke operators on \(\Gamma_0(m)\)
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros
• Low lying zeros of families of \(L\)-functions

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