Archimedean zeta integrals for the exterior square \(L\)-functions on \(\mathrm{GL}_{n}\)

DOI10.1016/J.JNT.2017.10.007zbMath1444.11100OpenAlexW2768248125MaRDI QIDQ1711706

Taku Ishii

Publication date: 18 January 2019

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2017.10.007

zbMATH Keywords

principal series representationsWhittaker functionsArchimedean zeta integralsautomorphic \(L\)-functions on \(\mathrm{GL}(n)\)

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (3)

The computation of multivariate archimedean zeta integrals on ${GL}_2 \times {GSp}_4$ and ${GL}_4$ ⋮ Test vectors for Archimedean period integrals ⋮ Rankin-Selberg \(L\)-functions via good sections

Cites Work

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• On the local Bump-Friedberg \(L\)-function. II
• On the residual spectrum of split classical groups supported in the Siegel maximal parabolic subgroup
• New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)
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• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• On the local and global exterior square \(L\)-functions of \(\mathrm{GL}_n\)
• Archimedean zeta integrals on \(\mathrm{GL}_n\times\mathrm{GL}_m\) and \(\mathrm{SO}_{2n+1}\times\mathrm{GL}_m\)
• Calculus of principal series Whittaker functions on \(\mathrm{SL}(n, \mathbb R)\)
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• The archimedean theory of the exterior square $L$-functions over $\mathbb{Q}$
• The Rankin–Selberg Method for Automorphic Distributions
• Langlands-Shahidi Method and Poles of Automorphic L-Functions: Application to Exterior Square L-Functions

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