Bingrong Huang (Tel-Aviv University)
Super-positivity of a family of L-functions

Zhiwei Yun and Wei Zhang introduced the notion of "super-positivity of self-dual L-functions" which specifies that all derivatives of the completed L-function at the central value s=1/2 should be non-negative. The Riemann Hypothesis implies super-positivity for self-dual cuspidal automorphic L-functions on GL(n). This talk is based on recent joint work with Dorian Goldfeld where we prove, for the first time, that there are infinitely many L-functions associated to modular forms for SL(2,Z) each of which has the super-positivity property.