Davenport-Hasse relations and an explicit Langlands correspondence, II : twisting conjectures

Colin J. Bushnell; Guy Henniart

Displaying similar documents to “Davenport-Hasse relations and an explicit Langlands correspondence, II : twisting conjectures”

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

Marie-France Vignéras (2000)

Journal de théorie des nombres de Bordeaux

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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...

An inequality for local unitary Theta correspondence

Z. Gong, L. Grenié (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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Given a representation $π$ of a local unitary group $G$ and another local unitary group $H$ , either the Theta correspondence provides a representation $θ_{H} (π)$ of $H$ or we set $θ_{H} (π) = 0$ . If $G$ is fixed and $H$ varies in a Witt tower, a natural question is: for which $H$ is $θ_{H} (π) \neq 0$ ? For given dimension $m$ there are exactly two isometry classes of unitary spaces that we denote $H_{m}^{\pm}$ . For $ε \in {0, 1}$ let us denote $m_{ε}^{\pm} (π)$ the minimal $m$ of the same parity of $ε$ such that $θ_{H_{m}^{\pm}} (π) \neq 0$ , then we prove that $m_{ε}^{+} (π) + m_{ε}^{-} (π) \geq 2 n + 2$ where $n$ is the dimension of $π$ .

Local tame lifting for $G L (N)$ . I: Simple characters

Colin J. Bushnell, Guy Henniart (1996)

Publications Mathématiques de l'IHÉS

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Numerical verification of the Stark-Chinburg conjecture for some icosahedral representations.

Jehanne, Arnaud, Roblot, Xavier-Francois, Sands, Jonathan (2003)

Experimental Mathematics

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Third symmetric power $L$ -functions for $G L (2)$

Freydoon Shahidi (1989)

Compositio Mathematica

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Galois representations

Richard Taylor (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Functoriality and the Inverse Galois problem II: groups of type $B_{n}$ and $G_{2}$

Chandrashekhar Khare, Michael Larsen, Gordan Savin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over $ℚ$ ? Let $ℓ$ be a prime and $t$ a positive integer. We show that that the finite simple groups of Lie type $B_{n} (ℓ^{k}) = 3 D S O_{2 n + 1} {(𝔽_{ℓ^{k}})}^{d e r}$ if $ℓ \equiv 3, 5 (mod 8)$ and $G_{2} (ℓ^{k})$ appear as Galois groups over $ℚ$ , for some $k$ divisible by $t$ . In particular, for each of the two Lie types and fixed $ℓ$ we construct infinitely many Galois groups but we do not have a precise...

A Stark conjecture “over $𝐙$ ” for abelian $L$ -functions with multiple zeros

Karl Rubin (1996)

Annales de l'institut Fourier

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Suppose $K / k$ is an abelian extension of number fields. Stark’s conjecture predicts, under suitable hypotheses, the existence of a global unit $ϵ$ of $K$ such that the special values $L^{'} (χ, 0)$ for all characters $χ$ of $Gal / (K / k)$ can be expressed as simple linear combinations of the logarithms of the different absolute values of $ϵ$ . In this paper we formulate an extension of this conjecture, to attempt to understand the values $L^{(r)} (χ, 0)$ when the order of vanishing $r$ may be greater than one. This conjecture...