Calculus of archimedean Rankin–Selberg integrals with recurrence relations

DOI10.1090/ert/618OpenAlexW3034047844WikidataQ114009920 ScholiaQ114009920MaRDI QIDQ5096470

Taku Ishii, Tadashi Miyazaki

Publication date: 17 August 2022

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.04095

zbMATH Keywords

Whittaker functionsRankin-Selberg methodprincipal seriesArchimedean zeta integrals

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (2)

Rankin-Selberg convolutions for \(\mathrm{GL}(n) \times \mathrm{GL}(n)\) and \(\mathrm{GL} (n) \times \mathrm{GL} (n -1)\) for principal series representations ⋮ Test vectors for Archimedean period integrals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical values of Rankin-Selberg \(L\)-functions for \(\mathrm{GL}_n \times \mathrm{GL}_{n-1}\) and the symmetric cube \(L\)-functions for \(\mathrm{GL}_2\)
• Gross-Zagier formula for \(\text{GL}_ 2\).
• New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)
• Whittaker newforms for archimedean representations of GL(2)
• Reducibility of generalized principal series representations
• On Whittaker vectors and representation theory
• Critical values of automorphic \(L\)-functions for \(\text{GL}(r)\times\text{GL}(r)\)
• Archimedean \(L\)-factors on \(\text{GL}(n)\times\text{GL}(n)\) and generalized Barnes integrals
• The local zeta integrals for \(\mathrm{GL}(2,\mathbb{C})\times \mathrm{GL}(2,\mathbb{C})\)
• Lectures on automorphic \(L\)-functions
• Archimedean zeta integrals on \(\mathrm{GL}_n\times\mathrm{GL}_m\) and \(\mathrm{SO}_{2n+1}\times\mathrm{GL}_m\)
• Automorphic forms on GL (2)
• Automorphic forms on \(\mathrm{GL}(2)\). Part II
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• The nonvanishing hypothesis at infinity for Rankin-Selberg convolutions
• WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT -FUNCTIONS
• Rankin-Selberg Convolutions
• Symmetry, Representations, and Invariants
• Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2)
• On the nonvanishing hypothesis for Rankin-Selberg convolutions for 𝐺𝐿_{𝑛}(ℂ)×𝔾𝕃_{𝕟}(ℂ)
• On the Symmetric Tensor Operators of the Unitary Groups

This page was built for publication: Calculus of archimedean Rankin–Selberg integrals with recurrence relations