Simultaneous nonvanishing of automorphic \(L\)-functions at the central point

DOI10.1007/S00229-010-0396-7zbMath1230.11062OpenAlexW1976501263MaRDI QIDQ625495

Zhao Xu

Publication date: 17 February 2011

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-010-0396-7

zbMATH Keywords

automorphic \(L\)-functioncentral pointsimultaneous nonvanishing

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)

Related Items (6)

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 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 ⋮ Simultaneous non-vanishing of quadratic Dirichlet \(L\)-functions and twists of Hecke \(L\)-functions

Cites Work

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• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• The central value of the Rankin-Selberg \(L\)-functions
• Heegner points, cycles and Maass forms
• A quadratic divisor problem
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• The cubic moment of central values of automorphic \(L\)-functions
• Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications.
• On sums of Hecke series in short intervals
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Rankin-Selberg \(L\)-functions in the level aspect.
• Low-lying zeros of dihedral \(L\)-functions
• On the positivity of the central critical values of automorphic \(L\)-functions for \(GL(2)\)
• Average values of modular \(L\)-series via the relative trace formula
• A new bound K2/3+  for Rankin-Selberg L-functions for Hecke congruence subgroups
• PETERSSON'S CONJECTURE FOR CUSP FORMS OF WEIGHT ZERO AND LINNIK'S CONJECTURE. SUMS OF KLOOSTERMAN SUMS
• The spectral growth of automorphic L-functions.
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros
• Nonvanishing of \(L\)-values and the Weyl law

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