On the nonvanishing hypothesis for Rankin-Selberg convolutions for $\mathrm {GL}_n(\mathbb {C})\times \mathrm {GL}_n(\mathbb {C})$
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.
متن کاملModal $\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\tilde{\mathrm{l}}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{C}$ Logics and Predicate Superintuitionistic Logics: $\mathrm{C}_{0\Gamma \mathrm{r}\mathrm{e}..\mathrm{S}},\mathrm{p}$
In this note we deal with intuitionistic modal logics over $\mathcal{M}\mathcal{I}PC$ and predicate superintuitionistic logics. We study the correspondence between the lattice of all (normal) extensions of MTPC and the lattice of all predicate superintuitionistic logics. Let $\mathrm{L}_{Prop}$ denote a propositional language which contains two modal operators $\square$ and $\mathrm{O}$ , and $...
متن کاملNonvanishing of certain Rankin-Selberg L-functions
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...
متن کاملOn the Poles of Rankin-selberg Convolutions of Modular Forms
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 ...
متن کاملStrong exponent bounds for the local Rankin-Selberg convolution
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2017
ISSN: 1088-4165
DOI: 10.1090/ert/502