Results 21 to 30 of about 671 (55)

On the ramification of modular parametrizations at the cusps

, 2018
We investigate the ramification of modular parametrizations of elliptic curves over Q at the cusps. We prove that if the modular form associated to the elliptic curve has minimal level among its twists by Dirichlet characters, then the modular ...
Brunault, François
core   +1 more source

Cuspidal ${\ell }$ -modular representations of $\operatorname {GL}_n({ F})$ distinguished by a Galois involution

Forum of Mathematics, Sigma
Let ${ F}/{ F}_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq 2$ with Galois automorphism $\sigma $ , and let R be an algebraically closed field of characteristic $\ell ...
Robert Kurinczuk, Nadir Matringe, Vincent Sécherre   +2 more
doaj   +1 more source

The spectral decomposition of shifted convolution sums

, 2007
We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.Comment: 15 pages, LaTeX2e; v2: corrected and slightly expanded ...
Blomer, Valentin, Harcos, Gergely
core   +1 more source

Decomposition of splitting invariants in split real groups

, 2010
To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of their endoscopic ...
Agaoka, Demazure, Langlands, Langlands, Langlands, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Shelstad, Springer, Tasho Kaletha   +14 more
core   +1 more source

Local parameters of supercuspidal representations

Forum of Mathematics, Pi
For a connected reductive group G over a nonarchimedean local field F of positive characteristic, Genestier-Lafforgue and Fargues-Scholze have attached a semisimple parameter ${\mathcal {L}}^{ss}(\pi )$ to each irreducible representation $\pi $
Wee Teck Gan, Michael Harris, Will Sawin, Raphaël Beuzart-Plessis   +3 more
doaj   +1 more source

Doubling constructions and tensor product L-functions: coverings of the symplectic group

Forum of Mathematics, Sigma
In this work, we develop an integral representation for the partial L-function of a pair $\pi \times \tau $ of genuine irreducible cuspidal automorphic representations, $\pi $ of the m-fold covering of Matsumoto of the symplectic group $
Eyal Kaplan
doaj   +1 more source

Twisting formula of epsilon factors

, 2017
For characters of a non-Archimedean local field we have explicit formula for epsilon factors. But in general, we do not have any generalized twisting formula of epsilon factors.
Biswas, Sazzad Ali
core   +1 more source

L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Forum of Mathematics, Sigma
Let $\pi $ be a cuspidal, cohomological automorphic representation of an inner form G of $\operatorname {{PGL}}_2$ over a number field F of arbitrary signature. Further, let $\mathfrak {p}$ be a prime of F such that G is split at
Lennart Gehrmann, Maria Rosaria Pati
doaj   +1 more source

Theta functions, fourth moments of eigenforms and the sup-norm problem II

Forum of Mathematics, Pi
Let f be an $L^2$ -normalized holomorphic newform of weight k on $\Gamma _0(N) \backslash \mathbb {H}$ with N squarefree or, more generally, on any hyperbolic surface $\Gamma \backslash \mathbb {H}$ attached to an Eichler order of ...
Ilya Khayutin, Paul D. Nelson, Raphael S. Steiner   +2 more
doaj   +1 more source

Eisenstein Cohomology for $\mathrm {GL}_N$ and the special values of Rankin–Selberg L-functions over a totally imaginary number field

Forum of Mathematics, Sigma
This article presents new rationality results for the ratios of critical values of Rankin–Selberg L-functions of $\mathrm {GL}(n) \times \mathrm {GL}(n')$ over a totally imaginary field $F.$ The proof is based on a cohomological ...
A. Raghuram
doaj   +1 more source