Yongyi Chen (Boston College)

Given an automorphic representation for an even unitary group U(n) over the function field of a smooth projective curve X over a finite field, and let’s say you want to know what the r-th central derivative of its base change L-function is. In this talk, we won’t quite get an explicit complex number, but we will instead state an equality between this central derivative and the intersection number between a Chow-valued theta lift of an automorphic form and another special cycle on the moduli stack of shtukas for U(n). We then prove this equality in the case n=2. Our approach stands in contrast to the relative trace formula approach of Yun-Zhang for PGL(2). This work uses, in an essential way, the special cycles and generating series of Feng-Yun-Zhang, which will also be discussed in this talk.