Simultaneous nonvanishing of 𝐺𝐿(2)×𝐺𝐿(2) and 𝐺𝐿(2) 𝐿-functions

DOI10.1090/S0002-9939-2014-12066-1zbMath1294.11054MaRDI QIDQ5418512

Sheng-Chi Liu

Publication date: 4 June 2014

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

zbMATH Keywords

\(L\)-functionnonvanishingGL(2)Hecke cusp form

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Zeta and (L)-functions: analytic theory (11M99)

Related Items (5)

Simultaneous non-vanishing of central values of \(\mathrm{GL}(2) \times \mathrm{GL}(3)\) and \(\mathrm{GL}(3)\) \(L\)-functions ⋮ Non-vanishing of the first derivative of GL(3) ×GL(2) L-functions ⋮ Simultaneous nonvanishing of automorphic \(L\)-functions ⋮ Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke–Maass L-functions in the critical strip ⋮ Simultaneous non-vanishing of quadratic Dirichlet \(L\)-functions and twists of Hecke \(L\)-functions

Cites Work

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• Simultaneous nonvanishing of automorphic \(L\)-functions at the central point
• The central value of the Rankin-Selberg \(L\)-functions
• Bilinear forms in the Fourier coefficients of half-integral weight cusp forms and sums over primes
• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• A non-vanishing theorem for zeta functions of \(\mathrm{GL}_n\)
• A nonvanishing result for twists of \(L\)-functions of \(\text{GL}(n)\)
• Nonvanishing of \(L\)-functions for \(\text{GL}(n,\mathbf A_Q)\)
• Average values of modular \(L\)-series via the relative trace formula
• Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions

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