Periods and nonvanishing of central \(L\)-values for \(\mathrm{GL}(2n)\)

DOI10.1007/s11856-018-1657-5zbMath1458.11078arXiv1308.2253OpenAlexW2963303659MaRDI QIDQ1650036

Brooke Feigon, Kimball Martin, David J. Whitehouse

Publication date: 29 June 2018

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.2253

zbMATH Keywords

periods of automorphic formsrelative trace formuladistinguished representationJacquet-Langlands correspondence, base change

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) 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)

Related Items (12)

An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of \((\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})\) ⋮ Epsilon dichotomy for linear models ⋮ On the fine expansion of the unipotent contribution of the Guo-Jacquet trace formula ⋮ Distinction of the Steinberg representation and a conjecture of Prasad and Takloo-Bighash ⋮ Multiplicity one for the pair \((\mathrm{GL}_n (D), \mathrm{GL}_n (E))\) ⋮ Local root numbers, Bessel models, and a conjecture of Guo and Jacquet ⋮ A mild Tchebotarev theorem for GL\((n)\) ⋮ The action of a mirabolic subgroup on a symmetric variety ⋮ A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles ⋮ Classification of standard modules with linear periods ⋮ On the residue method for period integrals ⋮ An infinitesimal variant of the Guo-Jacquet trace formula. II

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local root numbers, Bessel models, and a conjecture of Guo and Jacquet
• A mild Tchebotarev theorem for GL\((n)\)
• Fourier transform and the global Gan-Gross-Prasad conjecture for unitary groups
• Simple supercuspidal representations of \(\mathrm{GL}(n)\)
• Representations of \(GL(n)\) and division algebras over a p-adic field
• On representations distinguished by unitary groups
• Generalized Harish-Chandra descent, Gelfand pairs, and an Archimedean analog of Jacquet-Rallis's theorem. With an appendix by the authors and Eitan Sayag.
• Local periods for discrete series representations
• Shalika periods on \(\mathrm{GL}_2(D)\) and \(\mathrm{GL}_4\)
• Local Shalika models and functoriality
• Uniqueness of generalized Waldspurger model for \(GL(2n)\)
• Stabilization of periods of Eisenstein series and Bessel distributions on \(GL(3)\) relative to \(U(3)\)
• On central critical values of the degree four \(L\)-functions for \(\mathrm{GSp}(4)\): a simple trace formula
• An orthogonality relation for spherical characters of supercuspidal representations
• Relating invariant linear form and local epsilon factors via global methods. (With an appendix by Hiroshi Saito)
• On special Bessel periods and the Gross-Prasad conjecture for \(\mathrm {SO}(2n+1) \times \mathrm {SO}(2)\)
• Positivity of quadratic base change $L$-functions
• Linear periods.
• Globalization of Distinguished Supercuspidal Representations of GL(n)
• On the smooth transfer for Guo–Jacquet relative trace formulae
• Generalised form of a conjecture of Jacquet and a local consequence
• Spherical characters: the supercuspidal case
• Sur un résultat de Waldspurger
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• On the Decomposition of a Representation of SO_n When Restricted to SO_n-1
• On Irreducible Representations of So_2n+1 × So_2m
• Spherical Characters on p-Adic Symmetric Spaces
• On a Generalization of a Result of Waldspurger
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Unitary dual ofGL(n) at archimedean places and global Jacquet–Langlands correspondence
• Bessel models for GSp(4)
• Automorphic period and the central value of Rankin-Selberg L-function
• Central L-Values and Toric Periods for GL(2)

This page was built for publication: Periods and nonvanishing of central \(L\)-values for \(\mathrm{GL}(2n)\)