Determination of \(\text{GL}(3)\) cusp forms by central values of \(\text{GL}(3)\times \text{GL}(2)\, L\)-functions, level aspect

DOI10.1016/j.jnt.2011.01.014zbMath1272.11068OpenAlexW2055477620MaRDI QIDQ538163

Sheng-Chi Liu

Publication date: 23 May 2011

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.01.014

zbMATH Keywords

central values of \(L\)-functionsmultiplicity one theorem

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (9)

Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions ⋮ On effective determination of symmetric-square lifts, level aspect ⋮ On effective determination of cusp forms by \(L\)-values, level aspect ⋮ Central values of GL(2) ×GL(3) Rankin–Selberg L-functions ⋮ High order of accuracy difference schemes for the inverse elliptic problem with Dirichlet condition ⋮ On effective determination of symmetric-square lifts ⋮ On the effective determination of Maass cusp forms by \(L\)-values ⋮ Approximation of the inverse elliptic problem with mixed boundary value conditions and overdetermination ⋮ Twisted moments of GL(3) ×GL(2) L-functions

Uses Software

• GL(n)pack

Cites Work

• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions
• Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
• A non-vanishing theorem for zeta functions of \(\mathrm{GL}_n\)
• Special \(L\)-values of Rankin-Selberg convolutions
• Determination of modular forms by twists of critical \(L\)-values
• Modularity of the Rankin-Selberg \(L\)-series, and multiplicity one for \(\mathrm{SL}(2)\)
• Voronoi formulas on GL(n)
• On Euler Products and the Classification of Automorphic Representations I
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Determination of \(\text{GL}(3)\) cusp forms by central values of \(\text{GL}(3)\times \text{GL}(2)\, L\)-functions, level aspect