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}, pages = {171--271}, publisher = {Springer-Verlag}, volume = {111}, year = {2010}, doi = {10.1007/s10240-010-0025-8}, mrnumber = {2653249}, language = {en}, url = {http://archive.numdam.org/articles/10.1007/s10240-010-0025-8/} }
TY - JOUR AU - Michel, Philippe AU - Venkatesh, Akshay TI - The subconvexity problem for GL2 JO - Publications Mathématiques de l'IHÉS PY - 2010 SP - 171 EP - 271 VL - 111 PB - Springer-Verlag UR - http://archive.numdam.org/articles/10.1007/s10240-010-0025-8/ DO - 10.1007/s10240-010-0025-8 LA - en ID - PMIHES_2010__111__171_0 ER -
%0 Journal Article %A Michel, Philippe %A Venkatesh, Akshay %T The subconvexity problem for GL2 %J Publications Mathématiques de l'IHÉS %D 2010 %P 171-271 %V 111 %I Springer-Verlag %U http://archive.numdam.org/articles/10.1007/s10240-010-0025-8/ %R 10.1007/s10240-010-0025-8 %G en %F PMIHES_2010__111__171_0
Michel, Philippe; Venkatesh, Akshay. The subconvexity problem for GL2. Publications Mathématiques de l'IHÉS, Volume 111 (2010), pp. 171-271. doi : 10.1007/s10240-010-0025-8. http://archive.numdam.org/articles/10.1007/s10240-010-0025-8/
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