Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions

DOI10.1007/s00208-009-0380-2zbMath1234.11065OpenAlexW2022829084MaRDI QIDQ734964

Jyoti Sengupta, Satadal Ganguly, Jeffrey Hoffstein

Publication date: 14 October 2009

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-009-0380-2

zbMATH Keywords

modular formcentral valueapproximate functional equationRankin-Selberg L-functionPetersson trace formula

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 (22)

Some remarks on the critical values of Rankin-Selberg \(L\)-series ⋮ On effective determination of symmetric-square lifts, level aspect ⋮ Determination of cusp forms by central values of Rankin-Selberg \(L\)-functions ⋮ Zero-free regions for spectral averages of Hecke L-functions ⋮ On effective determination of cusp forms by \(L\)-values, level aspect ⋮ Central values of GL(2) ×GL(3) Rankin–Selberg L-functions ⋮ Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect ⋮ Non-vanishing of Rankin-Selberg convolutions for Hilbert modular forms ⋮ Determination of \(\mathrm{GL}(3)\) Hecke-Maass forms from twisted central values ⋮ First moments of Rankin-Selberg convolutions of automorphic forms on \(\mathrm{GL}(2)\) ⋮ Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: the weight aspect ⋮ Remarks on \(q\)-exponents of generalized modular functions ⋮ On the first moment of the symmetric-square 𝐿-function ⋮ 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 ⋮ Determining cusp forms by central values of Rankin-Selberg \(L\)-functions ⋮ Distinguishing newforms by their Hecke eigenvalues ⋮ Analytic number theory in India during 2001-2010 ⋮ Determining cuspforms from critical values of convolution L-functions and Rankin–Cohen brackets ⋮ Determination of ${\bf GL}(2)$ Maass forms from twists in the level aspect ⋮ A variant of multiplicity one theorems for half-integral weight modular forms

Cites Work

• 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.
• Symboles de Manin et valeurs de fonctions L
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions