The subconvexity problem for $\GL_{2}$

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.

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

References in corpus (3)

• Sparse equidistribution problems, period bounds, and subconvexity
• Convexity bounds for L-functions
• A Functional Equation for the Spectral Fourth Moment of Modular Hecke L-Functions

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