Seminar, Wei Zhang (MIT), Superpositivity of L-functions and 'completion of square', J250

Title: Superpositivity of L-functions and 'completion of square'

Abstract: We explain how the Riemann hypothesis and its generalization imply the positivity of the special values of all derivatives of normalized L-functions. This raises a question: can one interpret these positive values as squares? We present some examples of such interpretations, in the joint work with Xinyi Yuan and Shouwu Zhang over number fields on the Gross-Zagier formula, and with Zhiwei Yun over function fields on the Higher Gross-Zagier formula respectively.