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Let $k$ be a positive integer divisible by 4, $p > k$ a prime, $f$ an elliptic cuspidal eigenform (ordinary at $p$ ) of weight $k - 1$ , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives ${ad}^{0} M (- 1)$ and ${ad}^{0} M (2)$ , where $M$ is the motif attached to $f$ . More precisely, we prove that under certain conditions the $p$ -adic valuation of the algebraic part of the symmetric square $L$ -function of $f$ evaluated at $k$ provides a lower bound for the $p$ -adic valuation of the order of the Pontryagin...

Congruences modulo $ℓ$ between $ϵ$ factors for cuspidal representations of $G L (2)$

Marie-France Vignéras (2000)

Journal de théorie des nombres de Bordeaux

Let $ℓ \neq p$ be two different prime numbers, let $F$ be a local non archimedean field of residual characteristic $p$ , and let ${\bar{𝐐}}_{ℓ}, {\bar{𝐙}}_{ℓ}, {\bar{𝐅}}_{ℓ}$ be an algebraic closure of the field of $ℓ$ -adic numbers $𝐐_{ℓ}$ , the ring of integers of ${\bar{𝐐}}_{ℓ}$ , the residual field of ${\bar{𝐙}}_{ℓ}$ . We proved the existence and the unicity of a Langlands local correspondence over ${\bar{𝐅}}_{ℓ}$ for all $n \geq 2$ , compatible with the reduction modulo $ℓ$ in [V5], without using $L$ and $ϵ$ factors of pairs. We conjecture that the Langlands local correspondence over ${\bar{𝐐}}_{ℓ}$ respects congruences modulo $ℓ$ between...

Correction to the paper "On unitary representations of Jacobi groups".

Koichi Takase (1993)

Journal für die reine und angewandte Mathematik

Correspondence among Eisenstein series ... .

Young Ju Choie (1997)

Manuscripta mathematica

Coupling of universal monodromy representations of Galois-Teichmüller modular groups.

Hiroaki Nakamura (1996)

Mathematische Annalen

Differential and functional identities for the elliptic trilogarithm.

Strachan, Ian A.B. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Eisenstein series and Poincaré series for mixed automorphic forms.

Min Ho Lee (2000)

Collectanea Mathematica

Mixed automorphic forms generalize elliptic modular forms, and they occur naturally as holomorphic forms of the highest degree on families of abelian varieties parametrized by a Riemann surface. We construct generalized Eisenstein series and Poincaré series, and prove that they are mixed automorphic forms.

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A Dirichlet series for Hermitian modular forms of degree 2

A Dirichlet series for modular forms of degree n

A remark on Whittaker functions on SL $(n, ℝ)$

A spanning set for the space of super cusp forms.

An A4 extension of Q attached to a non-selfdual automorphic form on GL(3).

An integral representation of standard automorphic $L$ functions for unitary groups.

Automorphic forms and functions with respect to the Jacobi group.

Average values of L-series in function fields.

Configuration space of 8 points on the projective line and a 5-dimensional Picard modular group

Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture

Congruences modulo $ℓ$ between $ϵ$ factors for cuspidal representations of $G L (2)$

Correction to the paper "On unitary representations of Jacobi groups".

Correspondence among Eisenstein series ... .

Coupling of universal monodromy representations of Galois-Teichmüller modular groups.

Differential and functional identities for the elliptic trilogarithm.

Eisenstein series and Poincaré series for mixed automorphic forms.

Eisenstein series and zeta functions on symplectic groups.

Eisenstein series on four-dimensional hyperbolic space

Eisenstein series on quaternion Half-space.

Eisenstein series on quaternion half-space of degree N.

Currently displaying 1 – 20 of 85