Rankin–Selberg L-functions via good sections
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Yeongseong Jo
Abstract
In this article, we revisit Rankin–Selberg integrals established by Jacquet, Piatetski-Shapiro and Shalika. We prove the equality of Rankin–Selberg local factors defined with Schwartz–Bruhat functions and the factors attached to good sections, introduced by Piatetski-Shapiro and Rallis. Moreover, we propose a notion of exceptional poles in the framework of good sections. For cases of Rankin–Selberg, Asai and exterior square L-functions, the exceptional poles are consistent with well-known exceptional poles which characterize certain distinguished representations.
Acknowledgements
This paper owes its existence to a question raised by James Cogdell, who asked me whether Eisenstein series used to construct the integral representation of symmetric square L-functions could be adapted to the setting of Rankin–Selberg L-functions for
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Decomposition rank of approximately subhomogeneous C*-algebras
- Classification of indecomposable involutive set-theoretic solutions to the Yang–Baxter equation
- Degree bounds for modular covariants
- The Kobayashi–Royden metric on punctured spheres
- Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces
- Artin L-functions of almost monomial Galois groups
- Unitary representations with Dirac cohomology: A finiteness result for complex Lie groups
- Weighted sum formulas of multiple t-values with even arguments
- Long time behavior of solutions to 3D generalized MHD equations
- Bilinear forms on non-homogeneous Sobolev spaces
- Weyl and Zariski chambers on projective surfaces
- Rankin–Selberg L-functions via good sections
- Archimedean domains of skew generalized power series
Artikel in diesem Heft
- Frontmatter
- Decomposition rank of approximately subhomogeneous C*-algebras
- Classification of indecomposable involutive set-theoretic solutions to the Yang–Baxter equation
- Degree bounds for modular covariants
- The Kobayashi–Royden metric on punctured spheres
- Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces
- Artin L-functions of almost monomial Galois groups
- Unitary representations with Dirac cohomology: A finiteness result for complex Lie groups
- Weighted sum formulas of multiple t-values with even arguments
- Long time behavior of solutions to 3D generalized MHD equations
- Bilinear forms on non-homogeneous Sobolev spaces
- Weyl and Zariski chambers on projective surfaces
- Rankin–Selberg L-functions via good sections
- Archimedean domains of skew generalized power series
