Number Theory Seminar

A central problem in the theory of L-functions is to investigate their sizes on the critical line. The convexity bound, which follows from the Phragmen-Lindelof principle, is of little use in applications. Therefore much effort has been made to obtain subconvexity bounds for various L-functions, which have also been applied to give various equi-distribution results. In the classical case of the Riemann zeta-function, this convexity exponent is 1/4, and the classical subconvexity theorem of Weyl states that the 1/4 can be reduced to 1/6. In this talk, I will report a joint work with Yuk-Kam Lau and Yangbo Ye, in which we obtain a Weyl-like bound for Rankin-Selberg automorphic L-functions in the weight/eigenvalue aspect.