Intersection numbers and higher derivatives of L-functions for functions fields, I

Intersection numbers and higher derivatives of L-functions for functions fields, I

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Zhiwei Yun , Stanford University
Fine Hall 322

In joint work with Wei Zhang, we prove a higher derivative analogue of the Waldspurger formula and the Gross-Zagier formula in the function field setting under the assumption that the relevant objects are everywhere unramified. Our formula relates the self-intersection number of certain cycles on the moduli of Shtukas for GL(2) to higher derivatives of automorphic L-functions for GL(2). In this first talk, I will explain the geometric construction behind the formula.