Functoriality for the Classical Groups over Function Fields

Lomelí, Luis

doi:10.1093/imrn/rnp089

Cited by 13 publications

(55 citation statements)

References 31 publications

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“…Throughout this section, we restrict ourselves to the split case. Theorems 7.1 and 7.2 were established in [28,29] under the assumption char(k) = 2; we now remove this restriction. The corresponding results for the quasi-split unitary groups are proved in [31].…”

Section: On Functoriality For the Classical Groupsmentioning

confidence: 99%

“…The proof of the Ramanujan conjecture is essentially that of [28]. And the proofs of Properties (ii)-(iv) are those appearing in [29].…”

Section: On Functoriality For the Classical Groupsmentioning

confidence: 99%

“…Let us summarize the results of [28] on the globally generic functorial lift for the classical groups. Let G n be a split classical group of rank n defined over a global function field k. The functorial lift of [28] takes globally generic cuspidal automorphic representations π of G n (A k ) to automorphic representations of H N (A k ), where H N is chosen by the following table. Table 1 Theorem 7.2.…”

Section: On Functoriality For the Classical Groupsmentioning

confidence: 99%

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Rationality and holomorphy of Langlands–Shahidi L-functions over function fields

Lomelí

2018

Math. Z.

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We prove three main results: all Langlands-Shahidi automorphic L-functions over function fields are rational; after twists by highly ramified characters our automorphic L-functions become polynomials; and, if π is a globally generic cuspidal automorphic representation of a split classical group or a unitary group Gn and τ a cuspidal (unitary) automorphic representation of a general linear group, then L(s, π × τ ) is holomorphic for ℜ(s) > 1 and has at most a simple pole at s = 1. We also prove the holomorphy and non-vanishing of automorphic exterior square, symmetric square and Asai Lfunctions for ℜ(s) > 1. Finally, we complete previous results on functoriality for the classical groups over function fields.2010 Mathematics Subject Classification. Primary 11F70, 22E50, 22E55.

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Section: On Functoriality For the Classical Groupsmentioning

confidence: 99%

“…The proof of the Ramanujan conjecture is essentially that of [28]. And the proofs of Properties (ii)-(iv) are those appearing in [29].…”

Section: On Functoriality For the Classical Groupsmentioning

confidence: 99%

Section: On Functoriality For the Classical Groupsmentioning

confidence: 99%

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Rationality and holomorphy of Langlands–Shahidi L-functions over function fields

Lomelí

2018

Math. Z.

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“…We refer to L. Lomelí's work in [Lomelí 2009;Henniart and Lomelí 2011], where the method is developed at least for classical groups. Definition 1.1.…”

Section: )mentioning

confidence: 99%

“…We let α denote the unique simple root in N . The method is now being developed for fields of positive characteristic mainly by Luis Lomelí with some collaboration by Guy Henniart (see [Lomelí 2009;Henniart and Lomelí 2011]). …”

Section: Comments On Stability Of γ -Functionsmentioning

confidence: 99%

On equality of arithmetic and analytic factors through local Langlands correspondence

Shahidi¹

2012

Pacific J. Math.

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In this article we pursue the problem of equality of Artin factors with those defined on the representation theoretic (analytic) side by the local Langlands correspondence. We propose a set of axioms for the factors on the analytic side which allows us to prove the equality of the factors. In the case of L-functions the equality can be proved in a number of cases appearing in the Langlands-Shahidi method since one of the axioms, stability under highly ramified twists, is already available for the L-functions coming from this method.

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On the Local Langlands Correspondence for Split Classical Groups Over Local Function Fields

Ganapathy¹,

Varma²

2015

J. Inst. Math. Jussieu

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We prove certain depth bounds for Arthur’s endoscopic transfer of representations from classical groups to the corresponding general linear groups over local fields of characteristic 0, with some restrictions on the residue characteristic. We then use these results and the method of Deligne and Kazhdan of studying representation theory over close local fields to obtain, under some restrictions on the characteristic, the local Langlands correspondence for split classical groups over local function fields from the corresponding result of Arthur in characteristic 0.

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Functoriality for the Classical Groups over Function Fields

Cited by 13 publications

References 31 publications

Rationality and holomorphy of Langlands–Shahidi L-functions over function fields

Rationality and holomorphy of Langlands–Shahidi L-functions over function fields

On equality of arithmetic and analytic factors through local Langlands correspondence

On the Local Langlands Correspondence for Split Classical Groups Over Local Function Fields

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