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The subconvexity problem for GL2

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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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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

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  1. Philippe Michel
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  2. Akshay Venkatesh
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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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