Understand
In his paper "Beyond Endoscopy," Langlands tries to understand functoriality via poles of L-functions.
- The following paper further investigates the analytic continuation of a L-function associated to a $GL_2$ automorphic form through the trace formula.
- Though the usual way to obtain the analytic continuation of an L-function is through its functional equation, this paper shows that by simply assuming the trace formula, the functional equation of the L-function may be recovered.
- This paper is a step towards understanding the analytic continuation of the L-function at the same time as capturing information about functoriality.
Built on
H., Iwaniec, Prime geodesic theorem
1984
Earlier work this paper cites.
J. Rogawski, Modular forms, the Ramanujan conjecture and the Jacquet- Langlands correspondence
1994
Earlier work this paper cites.
Gradshteyn & Ryzhik. Tables of Integrals, Series, and Products
2000
Earlier work this paper cites.
I.Kowalski, P.Michel, and J. Vanderkam Mollification of the fourth moment of automorphic L-functions and arithmetic applications
2000
Earlier work this paper cites.
Similar
I.Kowalski, P.Michel, and J. Vanderkam, Rankin-Selberg L-functions in the level aspect
2002
Cited alongside, same era.
H. Iwaniec and E. Kowalski, Analytic Number Theory
2004
Cited alongside, same era.
R. P. Langlands. Beyond endoscopy
2004
Cited alongside, same era.
A. Knightly & C. Li. A relative trace formula proof of the Petersson Trace formula
2006
Cited alongside, same era.
P.E. Herman Beyond endoscopy for the Symmetric Cube L-function and the Shimura Correspondence
Cited in the paper.
P.E. Herman A trace formula approach to S y m 2 ⊗ S y m 2 Sym^{2}\otimes Sym^{2}
Cited in the paper.
P.E. Herman Subconvexity for the Rankin-Selberg L-function in both levels
Cited in the paper.
B.C. Ngoö, Le lemme fondamental pour les algebres de Lie
Cited in the paper.
Z. Rudnick, Thesis: Poicare Series
Cited in the paper.
P. Sarnak. Comments on Langland’s Lecture
Cited in the paper.
A. Venkatesh. Limiting forms of the trace formula
Cited in the paper.
Then
A. Knightly & C. Li., Traces of Hecke operators
2006
Later among the works it cites.
2010
Later among the works it cites.
P.E. Herman Beyond Endoscopy for the Rankin-Selberg L-function
2011
Later among the works it cites.
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