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arXiv · 0903.3591

The subconvexity problem for $\GL_{2}$

Philippe Michel·Akshay Venkatesh
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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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Philippe Michel, Akshay Venkatesh. 2009-03-20. The subconvexity problem for $\GL_{2}$. https://doi.org/10.1007/s10240-010-0025-8

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