2012

The Functional Equation and Beyond Endoscopy

Herman, P. Edward

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

    Original

    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.

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