Modularity of the Rankin-Selberg L-Series, and Multiplicity One for SL(2)
نویسندگان
چکیده
منابع مشابه
Modularity of the Rankin-selberg L-series, and Multiplicity One for Sl(2)
Relevant objects and the strategy 9 3.2. Weak to strong lifting, and the cuspidality criterion 13 3.3. Triple product L-functions: local factors and holomorphy 15 3.4. Boundedness in vertical strips 18 3.5. Modularity in the good case 30 3.6. A descent criterion 32 3.7. Modularity in the general case 35 4. Applications 37 4.1. A multiplicity one theorem for SL(2) 37 4.2. Some new functional equ...
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We establish zero-free regions tapering as an inverse power of the analytic conductor for Rankin-Selberg L-functions on GLn×GLn′ . Such zero-free regions are equivalent to commensurate lower bounds on the edge of the critical strip, and in the case of L(s, π × π̃), on the residue at s = 1. As an application we show that a cuspidal automorphic representation on GLn is determined by a finite numbe...
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We establish zero-free regions tapering as an inverse power of the analytic conductor for Rankin-Selberg L-functions on GLn×GLn′ . Such zero-free regions are equivalent to commensurate lower bounds on the edge of the critical strip, and in the case of L(s,π× π̃), on the residue at s = 1. As an application we show that a cuspidal automorphic representation on GLn is determined by a finite number ...
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In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...
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In [7] A. Selberg axiomatized properties expected of L-functions and introduced the “Selberg class” which is expected to coincide with the class of all arithmetically interesting L-functions. We recall that an element F of the Selberg class S satisfies the following axioms. • In the half-plane σ > 1 the function F (s) is given by a Dirichlet series ∑∞n=1 aF (n)n with aF (1) = 1 and aF (n) ≪ǫ n ...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2000
ISSN: 0003-486X
DOI: 10.2307/2661379