The subconvexity problem for L-functions
Proceedings of the International Congress of Mathematicians, ICM 2018
Estimating the size of automorphic L-functions on the critical line is a centralproblem in analytic number theory. An easy consequence of the standard analyticproperties of the L-function is the convexity bound, whereas the generalised RiemannHypothesis predicts a much sharper bound. Breaking the convexity barrier is a hardproblem. The moment method has been used to surpass convexity in the case of Lfunctions of degree one and two. In this talk I will discuss a different method, whichhas been quite successful to settle certain longstanding open problems in the case ofdegree three.
Munshi, Ritabrata, "The subconvexity problem for L-functions" (2018). Conference Articles. 115.