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

DOI10.1016/j.jnt.2010.06.002zbMath1264.11041OpenAlexW1971658081MaRDI QIDQ708266

Qinghua Pi

Publication date: 11 October 2010

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.06.002

zbMATH Keywords

central valueRankin-Selberg \(L\)-functionsmultiplicity one theorem

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items

On effective determination of symmetric-square lifts, level aspect ⋮ Determination of cusp forms by central values of Rankin-Selberg \(L\)-functions ⋮ On effective determination of cusp forms by \(L\)-values, level aspect ⋮ Central values of GL(2) ×GL(3) Rankin–Selberg L-functions ⋮ Determination of \(\mathrm{GL}(3)\) Hecke-Maass forms from twisted central values ⋮ Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: the weight aspect ⋮ On effective determination of symmetric-square lifts ⋮ On the effective determination of Maass cusp forms by \(L\)-values ⋮ Determining cuspforms from critical values of convolution L-functions and Rankin–Cohen brackets

Cites Work

• Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions
• Special \(L\)-values of Rankin-Selberg convolutions
• Determination of modular forms by twists of critical \(L\)-values
• Rankin-Selberg \(L\)-functions in the level aspect.
• Low lying zeros of families of \(L\)-functions
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