Beyond endoscopy for the Rankin-Selberg L-function

@article{Herman2010BeyondEF,
  title={Beyond endoscopy for the Rankin-Selberg L-function},
  author={P. Edward Herman},
  journal={arXiv: Number Theory},
  year={2010}
}
  • P. E. Herman
  • Published 1 March 2010
  • Mathematics
  • arXiv: Number Theory
View PDF on arXiv
12 Citations
Highly Influential Citations
1
Background Citations
3
Methods Citations
1
Results Citations
1

12 Citations

Citation Type

Citation Type

Subconvexity for the Rankin-Selberg L-function in both levels
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The functional equation and beyond endoscopy
In his paper “Beyond endoscopy,” Langlands tries to understand functoriality via poles of L-functions. This paper further investigates the analytic continuation of an L-function associated to a GL2…
Nonabelian Fourier transforms for spherical representations
Braverman and Kahzdan have introduced an influential conjecture on local functional equations for general Langlands $L$-functions. It is related to L. Lafforgue's equally influential conjectural…
BEYOND ENDOSCOPY FOR THE RELATIVE TRACE FORMULA II: GLOBAL THEORY
  • Y. Sakellaridis
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2017
For the group $G=\operatorname{PGL}_{2}$ we perform a comparison between two relative trace formulas: on the one hand, the relative trace formula of Jacquet for the quotient $T\backslash G/T$ , where…
ANALYTIC EXPERIMENTS BEYOND ENDOSCOPY
1.1. The Functoriality conjecture. The project I wish to describe is in the context of the so-called Beyond Endoscopy proposal of R. Langlands in 2001 [8], which offers a way of attacking Langlands’…
On the Fourier Transform of Regularized Bessel Functions on Complex Numbers and Beyond Endoscopy Over Number Fields
  • Zhi Qi
  • Mathematics
    International Mathematics Research Notices
  • 2019
In this article, we prove certain Weber–Schafheitlin-type integral formulae for Bessel functions over complex numbers. A special case is a formula for the Fourier transform of regularized Bessel…
On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields
In this article, we prove certain Weber-Schafheitlin type integral formulae for Bessel functions over complex numbers. A special case is a formula for the Fourier transform of regularized Bessel…
Quadratic base change and the analytic continuation of the Asai L-function: A new trace formula approach
Abstract:Using Langlands's beyond endoscopy idea, we study the Asai $L$-function associated to a real quadratic field $\Bbb{K}/\Bbb{Q}$. We prove that the Asai $L$-function associated to a cuspidal…
Rankin–Selberg L-functions and “beyond endoscopy”
Let f and g be two holomorphic cuspidal Hecke eigenforms on the full modular group $$ \text {SL}_{2}({\mathbb {Z}}). $$ We show that the Rankin–Selberg L-function $$L(s, f \times g)$$ has no pole at…
A summation formula for the Rankin-Selberg monoid and a nonabelian trace formula
Let $F$ be a number field and let $\mathbb{A}_F$ be its ring of adeles. Let $B$ be a quaternion algebra over $F$ and let $\nu:B \to F$ be the reduced norm. Consider the reductive monoid $M$ over $F$…
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References

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Limiting forms of the trace formula
We carry out the first nontrivial cases of the limiting process proposed by Langlands in his manuscript Beyond Endoscopy, with technical variations that enable us to treat the limit unconditionally.…
Beyond Endoscopy and special forms on GL(2)
Abstract We carry out (with technical modifications) some cases of a procedure proposed by R. Langlands in Beyond Endoscopy. This gives a new proof of the classification of “dihedral forms” on GL(2),…
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In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic…
Spectral methods of automorphic forms
Introduction Harmonic analysis on the Euclidean plane Harmonic analysis on the hyperbolic plane Fuchsian groups Automorphic forms The spectral theorem. Discrete part The automorphic Green function…
Analytic Number Theory
Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large…
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