The subconvexity problem for $\GL_{2}$

Details The subconvexity problem for $\GL_{2}$ The subconvexity problem for $\GL_{2}$

2009-03-20

arxiv.org/abs/0903.3591v2

Publ. Math IHES, 111 (2010), no. 1, 171-280

Mathematics

Number Theory

Almost final version to appear in Publ. Math IHES. References updated.

Scientific paper

10.1007/s10240-010-0025-8

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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