scientific article; zbMATH DE number 947823

zbMath0876.11022arXivmath/9505206MaRDI QIDQ4716214

Stephen Gelbart

Publication date: 20 November 1996

Full work available at URL: https://arxiv.org/abs/math/9505206

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zbMATH Keywords

Paley-Wiener theoremArthur-Selberg trace formulaLanglands programtruncation parametersGL(2)spectral termsadelic reductive groupsbase change lifting of cuspidal representationsspectral kernel functions

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Langlands-Weil conjectures, nonabelian class field theory (11R39)

Related Items (12)

Explicit forms of the trace formula for \(\mathrm{GL}(2)\) ⋮ Central values of twisted base change \(L\)-functions associated to Hilbert modular forms ⋮ On the non-vanishing of the central value of certain \(L\)-functions: unitary groups ⋮ Analytic torsion of arithmetic quotients of the symmetric space \(\mathrm{SL} (n,\mathbb{R})/ \mathrm{SO}(n)\) ⋮ Zeta Functions for the Adjoint Action of GL(n) and Density of Residues of Dedekind Zeta Functions ⋮ Bias of root numbers for modular newforms of cubic level ⋮ Fourier expansions of \(\mathrm{GL}(2)\) newforms at various cusps ⋮ On the Euler characteristic of the discrete spectrum ⋮ On the distribution of Satake parameters of \(\text{GL}_2\) holomorphic cuspidal representations ⋮ Riemann’s zeta function and beyond ⋮ Limit multiplicities for \({\text{SL}}_2(\mathcal{O}_F)\) in \({\text{SL}}_2(\mathbb{R}^{r_1}\oplus\mathbb{C}^{R_2})\) ⋮ Quantitative analysis of the Satake parameters of \mathrm GL₂representations with prescribed local representations

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