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.Comment: Almost final version to appear in Publ. Math IHES. References
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