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Yangbo Ye

2013-07-26
10:00:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

First we will review holomorphic and Maass cusp forms for SL(2,Z) and congruence subgroups, their L-functions, and Petersson and Kuznetsov trace formulas. Next we will prove the convexity bound for these L-functions using the Phragmen-Lindelöff convexity principle. After recalling several classical results on subconvexity bounds, we will sketch a proof of a subconvexity bound for the Rankin-Selberg L-function L(s,fxg), where f and g are cusp forms for SL(2,Z). Then we will move on to Maass forms F for SL(3,Z) and a subconvexity bound for L(s,Fxg). Finally we will survey recent results on subconvexity bounds in various aspects.