The nonvanishing hypothesis at infinity for Rankin-Selberg convolutions
نویسندگان
چکیده
منابع مشابه
On the Nonvanishing Hypothesis for Rankin-selberg Convolutions
Inspired by Sun’s breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups GLn(R)×GLn−1(R) and GLn(C)×GLn−1(C), we confirm it for GLn(C)×GLn(C) at the central critical point.
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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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The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this ...
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Let $F$ be a non-Archimedean locally compact field. Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$. We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$. Using the Langlands...
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We recently established the holomorphic continuation and functional equation of the exterior square L-function for GL(n,Z), and more generally, the archimedean theory of the GL(n) exterior square L-function over Q. We refer the reader to our paper [15] for a precise statement of the results and their relation to previous work on the subject. The purpose of this note is to give an account of our...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2016
ISSN: 0894-0347,1088-6834
DOI: 10.1090/jams/855