Determination of cusp forms by central values of Rankin-Selberg \(L\)-functions

DOI10.1007/S10986-011-9147-ZzbMATH Open1294.11067OpenAlexW2002408675MaRDI QIDQ392981

Qinghua Pi

Publication date: 15 January 2014

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-011-9147-z

zbMATH Keywords

Laplace operatorEisenstein seriesRankin-Selberg \(L\)-functioncusp formMaass formKuznetsov trace formulaRankin convolution

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) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Hecke-Petersson operators, differential operators (one variable) (11F25)

Cites Work

• Determining cusp forms by central values of Rankin-Selberg \(L\)-functions
• Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions
• The central value of the Rankin-Selberg \(L\)-functions
• Special \(L\)-values of Rankin-Selberg convolutions
• Determination of modular forms by twists of critical \(L\)-values
• La conjecture de Weil. I
• Rankin-Selberg \(L\)-functions in the level aspect.
• Determination of GL(3) Cusp Forms by Central Values of GL(3) x GL(2) L-functions
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Related Items (7)

On effective determination of symmetric-square lifts, level aspect ⋮ On effective determination of cusp forms by \(L\)-values, level aspect ⋮ Unnamed Item ⋮ On effective determination of symmetric-square lifts ⋮ On the effective determination of Maass cusp forms by \(L\)-values ⋮ Determination of \(\text{GL}(3)\) cusp forms by central values of \(\text{GL}(3)\times \text{GL}(2)\, L\)-functions, level aspect ⋮ Determination of GL(3) Cusp Forms by Central Values of GL(3) x GL(2) L-functions

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