Petersson trace formula over newforms and subconvexity for triple product L-functions in cubic level

Subconvexity estimation is one of the most important and challenging problem in the field of analytic number theory and L-functions. In this talk, we will focus on the strong subconvexity bound in the level aspect. I will report on my recent joint work with Dr. H.Zhang which achieves the Weyl-type bound for triple product L-functions in the cubic level case. Our method is a combination of different tools in classical analytic number theory, automorphic forms and representation theory.