Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect

DOI10.1090/tran/6932zbMath1426.11048arXiv1609.07209OpenAlexW2963842159MaRDI QIDQ5367101

Naomi Tanabe, Alia Hamieh

Publication date: 12 October 2017

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

Full work available at URL: https://arxiv.org/abs/1609.07209

zbMATH Keywords

Hilbert modular formsRankin-Selberg convolutionPetersson trace formula

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 on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (2)

Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect ⋮ Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: the weight aspect

Cites Work

• Non-vanishing of \(L\)-functions of Hilbert modular forms at the central point
• Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions
• The special values of the zeta functions associated with Hilbert modular forms
• Special \(L\)-values of Rankin-Selberg convolutions
• Determination of modular forms by twists of critical \(L\)-values
• Poincaré series and Hilbert modular forms
• Determination of a \(\text{GL}_2\) automorphic cuspidal representation by twists of critical \(L\)-values
• Determining modular forms of general level by central values of convolution L-functions
• Notes on the arithmetic of Hilbert modular forms
• Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect
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