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


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Article Info

DATE

2019-02

AUTHORS

Luis Alberto Lomelí

ABSTRACT

We prove that all Langlands–Shahidi automorphic L-functions over function fields are rational; after twists by highly ramified characters they become polynomials; and, if π is a globally generic cuspidal automorphic representation of a split classical group or a unitary group and τ is 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 L-functions for R(s)>1. Finally, we complete previous results on functoriality for the classical groups over function fields with applications to the Ramanujan Conjecture and Riemann Hypothesis. More... »

PAGES

1-29

References to SciGraph publications

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  • 2000-12. Langlands-shahidi method and poles of automorphicL-functions II in ISRAEL JOURNAL OF MATHEMATICS
  • 1976. On the Functional Equations Satisfied by Eisenstein Series in NONE
  • 2002-01. Chtoucas de Drinfeld et correspondance de Langlands in INVENTIONES MATHEMATICAE
  • 1989-02. A unitarity criterion forp-adic groups in INVENTIONES MATHEMATICAE
  • 1976-02. A non-vanishing theorem for zeta functions ofGLn in INVENTIONES MATHEMATICAE
  • 1994-12. Unrefined minimal K-types forp-adic groups in INVENTIONES MATHEMATICAE
  • 2018-07. Types and unitary representations of reductive p-adic groups in INVENTIONES MATHEMATICAE
  • 1986-12. Representations of groups over close local fields in JOURNAL D'ANALYSE MATHÉMATIQUE
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    http://scigraph.springernature.com/pub.10.1007/s00209-018-2100-7

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