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A comparison of automorphic and Artin L-series of GL(2)-type agreeing at degree one primes

Martin, Kimball and Ramakrishnan, Dinakar (2016) A comparison of automorphic and Artin L-series of GL(2)-type agreeing at degree one primes. In: Advances in the theory of automorphic forms and their L-functions. Contemporary mathematics. No.664. American Mathematical Society , Providence, RI, pp. 339-350. ISBN 978-1-4704-1709-3.

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Let F/k be a cyclic extension of number fields of prime degree. Let ρ be an irreducible 2-dimensional representation of Artin type of the absolute Galois group of F, and π a cuspidal automorphic representation of GL_2(A_F), such that the L-functions L(s,ρ_v) and L(s,π_v) agree at all (but finitely many of) the places v of degree one over k. We prove in this case that we have the global identity L(s,ρ)=L(s,π), with ρ_v↔π_v being given by the local Langlands correspondence at all v. In particular, π is tempered and L(s,ρ) is entire.

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Additional Information:© 2016 American Mathematical Society. The first author was partially supported by Simons Collaboration Grant 240605. The second author was partially supported by NSF grant DMS-1001916.
Funding AgencyGrant Number
Simons Foundation240605
Series Name:Contemporary mathematics
Issue or Number:664
Classification Code:2010 Mathematics Subject Classification: Primary 11R39; Secondary 11F70, 11F80
Record Number:CaltechAUTHORS:20160707-080856277
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68877
Deposited By: Tony Diaz
Deposited On:08 Jul 2016 03:13
Last Modified:03 Oct 2019 10:17

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