Archimedean Theory and 𝜖-Factors for the Asai Rankin-Selberg Integrals

R Beuzart-Plessis - Relative Trace Formulas, 2021 - Springer
In this paper, we partially complete the local Rankin-Selberg theory of Asai L-functions and
𝜖-factors as introduced by Flicker and Kable. In particular, we establish the relevant local …

Supercuspidal representations of GLn (F) distinguished by a Galois involution

V Sécherre - Algebra & Number Theory, 2019 - msp.org
Abstract Let F∕ F 0 be a quadratic extension of nonarchimedean locally compact fields of
residual characteristic p≠ 2 and let σ denote its nontrivial automorphism. Let R be an …

Repr\'esentations cuspidales de GL (r, D) distingu\'ees par une involution int\'erieure

V Sécherre - arXiv preprint arXiv:2005.05615, 2020 - arxiv.org
Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue
characteristic p and G be an inner form of GL (2n, F). This is a group of the form GL (r, D) for …

Endo-parameters for p-adic classical groups

R Kurinczuk, D Skodlerack, S Stevens - Inventiones mathematicae, 2021 - Springer
For a classical group over a non-archimedean local field of odd residual characteristic p, we
prove that two cuspidal types, defined over an algebraically closed field CC of characteristic …

Modulo ℓ distinction problems

P Cui, T Lanard, H Lu - Compositio Mathematica, 2024 - cambridge.org
Let $ F $ be a non-archimedean local field of characteristic different from 2 and residual
characteristic $ p $. This paper concerns the $\ell $-modular representations of a connected …

Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups

D Liu, JJ Ma, F Shi - arXiv preprint arXiv:2208.02308, 2022 - arxiv.org
In this paper, we deduce explicit multiplicity formulas of the Fourier-Jacobi model for Deligne-
Lusztig characters of finite symplectic groups, unitary groups, and general linear groups. We …

Finite period vectors and Gauss sums

Y Jo - Finite Fields and Their Applications, 2024 - Elsevier
We study four sums including the Jacquet–Piatetski-Shapiro–Shalika, Flicker, Bump–
Friedberg, and Jacquet–Shalika sums associated to irreducible cuspidal representations of …

Supercuspidal representations of GLn (F) distinguished by an orthogonal involution

J Zou - Journal of Number Theory, 2022 - Elsevier
Let F be a non-archimedean locally compact field of residue characteristic p≠ 2, let G= GL n
(F) and let H be an orthogonal subgroup of G. For π a complex smooth supercuspidal …

Local exterior square and Asai L-functions for GL (n) in odd characteristic

Y Jo - Pacific Journal of Mathematics, 2023 - msp.org
Let F be a nonarchimedean local field of odd characteristic p> 0. We consider local exterior
square L-functions L (s, π,∧ 2), Bump–Friedberg L-functions L (s, π, BF⁡), and Asai L …

Cuspidal -modular representations of distinguished by a Galois involution

R Kurinczuk, N Matringe, V Sécherre - arXiv preprint arXiv:2310.15820, 2023 - arxiv.org
Let $ F/F_0 $ be a quadratic extension of non-Archimedean locally compact fields of
residual characteristic $ p\neq2 $ with Galois automorphism $\sigma $, and let $ R $ be an …