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.
@article{PMIHES_2010__111__171_0, author = {Michel, Philippe and Venkatesh, Akshay}, title = {The subconvexity problem for GL2}, journal = {Publications Math\'ematiques de l'IH\'ES}, volume = {112}, year = {2010}, pages = {171-271}, doi = {10.1007/s10240-010-0025-8}, mrnumber = {2653249}, language = {en}, url = {http://dml.mathdoc.fr/item/PMIHES_2010__111__171_0} }
Michel, Philippe; Venkatesh, Akshay. The subconvexity problem for GL2. Publications Mathématiques de l'IHÉS, Tome 112 (2010) pp. 171-271. doi : 10.1007/s10240-010-0025-8. http://gdmltest.u-ga.fr/item/PMIHES_2010__111__171_0/
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