Number Theory Seminar

The celebrated Gross-Zagier formula, under classical Heegner hypothesis, was established by Gross and Zagier. The general Gross-Zagier formula over Shimura curves was finally completed by Yuan, S. Zhang and W. Zhang via the arithmetic Siegel-Weil. On the other hand, W. Zhang has formulated a relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture. In this talk, we shall discuss a proof of Yuan-Zhang-Zhang's theorem via the relative trace formula approach under W. Zhang's framework. In particular, we shall talk about arithmetic smooth matching at archimedean places. This is a joint work with Y. Tian.