# 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
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## References

SHOWING 1-6 OF 6 REFERENCES
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),
Contributions to automorphic forms, geometry, and number theory
• Mathematics
• 2004
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
• Mathematics
• 2004
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