English

The subconvexity problem for $\GL_{2}$

Number Theory 2014-11-18 v2

Abstract

Generalizing and unifying prior results, we solve the subconvexity problem for the LL-functions of \GL1\GL_{1} and \GL2\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.

Keywords

Cite

@article{arxiv.0903.3591,
  title  = {The subconvexity problem for $\GL_{2}$},
  author = {Philippe Michel and Akshay Venkatesh},
  journal= {arXiv preprint arXiv:0903.3591},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T12:42:50.473Z