Some Structural Results for the Stability of Root Numbers

Sundaravaradhan, Rajan

doi:10.1093/imrn/rnm141

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…For n ∈ N H (w) we have m = µ(n) lies in a unique B-Bruhat cell in G ⊂ M H , call it C( w) = B wB and this is the Bruhat cell in G that intersects Im(µ) in a subset of highest possible dimension. From Proposition 3.2 in [10] (see also Remark 1.11 in [34]) we have the relation w = w 0 w. In our situation W. Kuo, in the case 2(b) in his appendix to [34], has used the analysis of [40] to compute w and w in our case. We have w = w ℓ and then w = w H ℓ as in (4.3).…”

Section: If We Let Bmentioning

confidence: 79%

“…For us w = w ℓ and this supports a Bessel function by the criterion in [9]. Also, Assumption 3.6 in [9] holds by the work of Sundaravaradhan [40].…”

Section: If We Let Bmentioning

confidence: 94%

“…From Proposition 3.2 in [10] (see also Remark 1.11 in [34]) we have the relation w = w 0w . In our situation W. Kuo, in the case 2(b) in his appendix to [34], has used the analysis of [40] to computew and w in our case. We havẽ w = w ℓ and then w = w H ℓ as in (4.3).…”

Section: If We Let Bmentioning

confidence: 99%

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Local Langlands correspondence for GLn and the exterior and symmetric square ε-factors

Cogdell¹,

Shahidi²,

Tsai³

2017

Duke Math. J.

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Abstract. Let F be a p-adic field, i.e., a finite extension of Q p for some prime p. The local Langlands correspondence attaches to each continuous n-dimensional Φ-semisimple representation ρ of W ′ F , the Weil-Deligne group for F /F , an irreducible admissible representation π(ρ) of GL n (F ) such that, among other things, the local L-and ε-factors of pairs are preserved. This correspondence should be robust and preserve various parallel operations on the arithmetic and analytic sides, such as taking the exterior square or symmetric square. In this paper, we show that this is the case for the local arithmetic and analytic symmetric square and exterior square ε-factors, that is, that ε(s,The agreement of the L-functions also follows by our methods, but this was already known by Henniart. The proof is a robust deformation argument, combined with local/global techniques, which reduces the problem to the stability of the analytic γ-factor γ(s, π, Λ 2 , ψ) under highly ramified twists when π is supercuspidal. This last step is achieved by relating the γ-factor to a Mellin transform of a partial Bessel function attached to the representation and then analyzing the asymptotics of the partial Bessel function, inspired in part by the theory of Shalika germs for Bessel integrals. The stability for every irreducible admissible representation π then follows from those of the corresponding arithmetic γ-factors as a corollary.

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Section: If We Let Bmentioning

confidence: 79%

“…For us w = w ℓ and this supports a Bessel function by the criterion in [9]. Also, Assumption 3.6 in [9] holds by the work of Sundaravaradhan [40].…”

Section: If We Let Bmentioning

confidence: 94%