Non-vanishing of $L$-functions of Hilbert modular forms inside the critical strip

DOI10.4064/aa170721-10-7zbMath1434.11097OpenAlexW2896070663MaRDI QIDQ4621502

Wissam Raji, Alia Hamieh

Publication date: 12 February 2019

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa170721-10-7

zbMATH Keywords

Poincaré seriesHilbert modular formsnon-vanishing of lfunctions

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Automorphic forms, one variable (11F12) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Applications of automorphic functions and forms to multiplicative problems (11N75)

Related Items (4)

Nonvanishing of kernel functions and Poincaré series for Jacobi forms ⋮ On quotients of derivatives of \(L\)-functions inside the critical strip ⋮ Non-vanishing of derivatives of \(L\)-functions of Hilbert modular forms in the critical strip ⋮ Simultaneous nonvanishing of products of \(L\)-functions associated to elliptic cusp forms

Cites Work

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• Non-vanishing of \(L\)-functions of Hilbert modular forms at the central point
• The special values of the zeta functions associated with Hilbert modular forms
• Nonvanishing of Hecke \(L\)-functions associated to cusp forms inside the critical strip
• Poincaré series and Hilbert modular forms
• Nonvanishing and central critical values of twisted \(L\)-functions of cusp forms on average
• Nonvanishing of Koecher-Maass series attached to Siegel cusp forms

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