Local Rankin-Selberg convolutions for 𝐺𝐿_{𝑛}: Explicit conductor formula

DOI10.1090/S0894-0347-98-00270-7zbMath0899.22017OpenAlexW1730923064MaRDI QIDQ4396477

Colin J. Bushnell, Guy Henniart, Philip C. Kutzko

Publication date: 14 June 1998

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

Full work available at URL: https://doi.org/10.1090/s0894-0347-98-00270-7

zbMATH Keywords

non-Archimedean local fieldconductor formulalocal constantirreducible smooth representationslocal Rankin-Selberg convolutions

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50)

Related Items (27)

Explicit Plancherel formula for the \(p\)-adic group GL(\(n\)) ⋮ On an inequality of Bushnell-Henniart for Rankin-Selberg conductors ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The Langlands-Shahidi method for pairs via types and covers ⋮ Rankin-Selberg gamma factors of level zero representations of \(\mathrm{GL}_{n}\) ⋮ Equidistribution theorems for holomorphic Siegel modular forms for \(\mathrm{GSp}_4\); Hecke fields and \(n\)-level density ⋮ On Swan exponents of symmetric and exterior square Galois representations ⋮ Automorphic tensor products and cuspidal cohomology of the GL4 ⋮ On the growth of cuspidal cohomology of \(\mathrm{GL}(2)\) and \(\mathrm{GL}(3)\) ⋮ Sums of twisted GL(2) \(L\)-functions over function fields. ⋮ Langlands parameters for epipelagic representations of \(\mathrm{GL}_n\) ⋮ Unnamed Item ⋮ Holomorphy of Rankin triple \(L\)-functions; special values and root numbers for symmetric cube \(L\)-functions ⋮ Davenport-Hasse relations and an explicit Langlands correspondence. II: Twisting conjectures. ⋮ Plancherel measure for GL(\(n,F\)) and GL(\(m,D\)): Explicit formulas and Bernstein decomposition ⋮ Proof of the Tadić conjecture (U0) on the unitary dual of GL m (D) ⋮ Local Langlands correspondence and ramification for Carayol representations ⋮ Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations. II: Wild case ⋮ To an effective local Langlands Corrspondence ⋮ Explicit Whittaker data for essentially tame supercuspidal representations ⋮ Supercuspidal representations of GL\(_n\): Explicit Whittaker functions ⋮ A construction method for induced types and its application to \(G_2\) ⋮ An explicit conductor formula for \(\operatorname{GL}_n\times\operatorname{GL}_1\) ⋮ Correspondance de Langlands locale pour GLn et conducteurs de paires ⋮ Bounds for Rankin–Selberg integrals and quantum unique ergodicity for powerful levels ⋮ Towards the Jacquet conjecture on the local converse problem for \(p\)-adic \(\mathrm {GL}_n\)

Cites Work

• Unnamed Item
• Conducteur des représentations du groupe linéaire
• Characterization of the local Langlands conjecture by \(\varepsilon\)-factors for pairs
• Local tame lifting for \(GL(N)\). I: Simple characters
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• Zeta functions of simple algebras
• Rankin-Selberg Convolutions
• The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129)
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• Hereditary orders, Gauss sums and supercuspidal representations of GLN.
• On Certain L-Functions
• Smooth representations of reductive p -ADIC groups: structure theory via types

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