Critical values of Rankin-Selberg \(L\)-functions for \(\mathrm{GL}_n \times \mathrm{GL}_{n-1}\) and the symmetric cube \(L\)-functions for \(\mathrm{GL}_2\)

DOI10.1515/forum-2014-0043zbMath1417.11082arXiv1312.5955OpenAlexW2962835034MaRDI QIDQ280781

Publication date: 10 May 2016

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.5955

zbMATH Keywords

automorphic \(L\)-functions critical values cohomology of arithmetic groups

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Cohomology of arithmetic groups (11F75)

Related Items (19)

Relations of rationality for special values of Rankin-Selberg \(L\)-functions of \(\mathrm{GL}_n \times \mathrm{GL}_m\) over CM-fields ⋮ On Deligne's conjecture for symmetric fifth \(L\)-functions of modular forms ⋮ Rationality for isobaric automorphic representations: the CM-case ⋮ On algebraicity of special values of symmetric 4-th and 6-th power \(L\)-functions for \(\operatorname{GL}(2)\) ⋮ Archimedean non-vanishing, cohomological test vectors, and standard \(L\)-functions of \(\mathrm{GL}_{2n}\): complex case ⋮ Calculus of archimedean Rankin–Selberg integrals with recurrence relations ⋮ On the nonvanishing hypothesis for Rankin-Selberg convolutions for 𝐺𝐿_{𝑛}(ℂ)×𝔾𝕃_{𝕟}(ℂ) ⋮ Algebraicity of the central critical values of twisted triple product \(L\)-functions ⋮ On Deligne's conjecture for symmetric fourth \(L\)-functions of Hilbert modular forms ⋮ Rationality results for the exterior and the symmetric square \(L\)-function (with an appendix by Nadir Matringe) ⋮ On period relations for automorphic 𝐿-functions I ⋮ L-functions of GL_2n: p-adic properties and non-vanishing of twists ⋮ Algebraicity of the near central non-critical values of symmetric fourth \(L\)-functions for Hilbert modular forms ⋮ Sums of Galois representations and arithmetic homology ⋮ On the growth of cuspidal cohomology of \(\operatorname{GL}_4\) ⋮ Cohomological Representations and Functorial Transfer from Classical Groups ⋮ Critical values of \(L\)-functions for \(\mathrm{GL}_3 \times \mathrm{GL}_1\) and symmetric square \(L\)-functions for \(\mathrm{GL}_2\) over a CM field ⋮ The nonvanishing hypothesis at infinity for Rankin-Selberg convolutions ⋮ A cohomological interpretation of Archimedean zeta integrals for \(\mathrm{GL}_3\times\mathrm{GL}_2\)

This page was built for publication: Critical values of Rankin-Selberg \(L\)-functions for \(\mathrm{GL}_n \times \mathrm{GL}_{n-1}\) and the symmetric cube \(L\)-functions for \(\mathrm{GL}_2\)