Nonvanishing of the central \(L\)-values with large weight

DOI10.1016/j.aim.2015.08.009zbMath1385.11030OpenAlexW1129512186MaRDI QIDQ887303

Wenzhi Luo

Publication date: 28 October 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2015.08.009

zbMATH Keywords

central \(L\)-valueholomorphic Hecke eigenformlarge weightpositive proportion nonvanishing

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11)

Related Items (13)

Mollification and non-vanishing of automorphic \(L\)-functions on \(\mathrm{GL}(3)\) ⋮ Nonvanishing of central \(L\)-values of Maass forms ⋮ Moments of central 𝐿-values for Maass forms over imaginary quadratic fields ⋮ The first moment of central values of symmetric square \(L\)-functions in the weight aspect ⋮ COUNTING HECKE EIGENFORMS WITH NONVANISHING -VALUE ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ On simultaneous nonvanishing of the central $L$-values ⋮ Extreme values of L$L$‐functions of newforms ⋮ Non-vanishing of Maass form $L$-functions at the central point ⋮ On central \(L\)-derivative values of automorphic forms ⋮ Moments of \(L\)-functions and the Liouville-Green method ⋮ Non-vanishing of the derivative of \(L\)-functions at the central point ⋮ Cuspidal projections of products of Eisenstein series

Cites Work

• Unnamed Item
• 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
• Nonvanishing of \(L\)-values and the Weyl law

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