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The subconvexity problem for GL2

Publications mathématiques de l'IHÉS volume 111, pages 171–271 (2010)Cite this article

Abstract

Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL 1 and GL 2 automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino–Ikeda.

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Author information

Authors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Philippe Michel

  2. Université Montpellier II, Montpellier, France

    Philippe Michel

  3. Stanford University, Stanford, USA

    Akshay Venkatesh

Authors
  1. Philippe Michel
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  2. Akshay Venkatesh
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Corresponding author

Correspondence to Philippe Michel.

Additional information

P. Michel was partially supported by the advanced research grant n. 228304 from the European Research Council and the SNF grant 200021-12529.

A. Venkatesh was partially supported by the Sloan foundation, the Packard Foundation and by an NSF grant.

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Michel, P., Venkatesh, A. The subconvexity problem for GL2 . Publ.math.IHES 111, 171–271 (2010). https://doi.org/10.1007/s10240-010-0025-8

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  • DOI: https://doi.org/10.1007/s10240-010-0025-8

Keywords

  • Eisenstein Series
  • Automorphic Form
  • Sobolev Norm
  • Automorphic Representation
  • Cuspidal Representation