On the non-vanishing of cubic twists of automorphic $L$-series

DOI10.1090/S0002-9947-99-02082-6zbMath0926.11033OpenAlexW1523181933MaRDI QIDQ4226665

Xiaotie She

Publication date: 27 January 1999

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02082-6

zbMATH Keywords

nonvanishingRankin-Selberg convolutionmetaplectic Eisenstein seriescubic twistsautomorphic \(L\)-series

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Applications of automorphic functions and forms to multiplicative problems (11N75)

Cites Work

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• Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivatives
• Cubic metaplectic forms on GL(3)
• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• Mean values of derivatives of modular \(L\)-series
• On the derivatives of theta functions and modular forms
• Nonvanishing of \(L\)-series associated to cubic twists of elliptic curves
• Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• A cubic analogue of the theta series. II.
• On the imaginary quadratic Doi-Naganuma lifting of modular forms of arbitrary level
• Correspondances de Shimura et quaternions
• On the order of vanishing of modular $L$-functions at the critical point

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