On central \(L\)-derivative values of automorphic forms

DOI10.1007/s00209-017-1936-6zbMath1448.11097OpenAlexW2761988026MaRDI QIDQ1745333

Shenhui Liu

Publication date: 17 April 2018

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-017-1936-6

zbMATH Keywords

nonvanishingmollifiersHeegner cyclesholomorphic Hecke eigenformscentral \(L\)-derivative values

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11)

Related Items (3)

Nonvanishing of central \(L\)-values of Maass forms ⋮ Moments of central 𝐿-values for Maass forms over imaginary quadratic fields ⋮ The fourth moment of derivatives of Dirichlet \(L\)-functions in function fields

Uses Software

• DLMF

Cites Work

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• Nonvanishing of the central \(L\)-values with large weight
• On the central value of symmetric square \(L\)-functions
• Heegner points and derivatives of \(L\)-series
• Heegner points and derivatives of \(L\)-series. II
• Jacobi forms and a certain space of modular forms
• Heights of Heegner cycles and derivatives of L-series
• Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications.
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Rankin-Selberg \(L\)-functions in the level aspect.
• The critical order of vanishing of automorphic \(L\)-functions with large level
• Non-vanishing of high derivatives of Dirichlet \(L\)-functions at the central point
• The rank of quotients of \(J_0(N)\)
• The analytic rank of \(J_0(q)\) and zeros of automorphic \(L\)-functions.
• Gross-Kohnen-Zagier theorem for higher weight forms
• The first moment of cusp form $L$-functions in weight aspect on average
• Non-vanishing of the symmetric square L -function at the central point
• A lower bound for the rank of $J_0(q)$
• Non-vanishing of high derivatives of automorphic L-functions at the center of the critical strip
• A mean square formula for central values of twisted automorphic L-functions
• A density theorem on automorphic $L$-functions and some applications
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros

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