A Converse Theorem for Epsilon Factors

Kameswari, P. Anuradha; Tandon, Rajat

doi:10.1006/jnth.2000.2619

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Counting the Twists When K /F Is Ramified1

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Cited by 4 publications

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“…It is known (see, for instance, §3 of [2]) that if d is odd then d = 2t + 1 and there exists a uniformizer, denoted by π K such that tr π K = 0. Let x 0 = π K .…”

Section: Counting the Twists When K /F Is Ramifiedmentioning

confidence: 99%

On counting twists of a character appearing in its associated Weil representation

Namboothiri

2011

Proc Math Sci

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Abstract. Consider an irreducible, admissible representation π of GL(2,F ) whose restriction to GL(2,F )+ breaks up as a sum of two irreducible representations π + + π − . If π = r θ , the Weil representation of GL(2,F ) attached to a character θ of K * which does not factor through the norm map from K to F , then χ ∈ K * with (χ.θ −1 )| F * = ω K/F occurs in r θ + if and only if ǫ(θχ −1 , ψ 0 ) = ǫ(θχ −1 , ψ 0 ) = 1 and in r θ − if and only if both the epsilon factors are −1. But given a conductor n, can we say precisely how many such χ will appear in π? We calculate the number of such characters at each given conductor n in this work.

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“…It is known (see, for instance, §3 of [2]) that if d is odd then d = 2t + 1 and there exists a uniformizer, denoted by π K such that tr π K = 0. Let x 0 = π K .…”

Section: Counting the Twists When K /F Is Ramifiedmentioning

confidence: 99%