Number theory: Shtukas and the Taylor expansion of L-functions

Wei Zhang

Zhiwei Yun

Shtukas and the Taylor expansion of L-functions

Abstract. We define the Heegner–Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with r-modifications for an even integer r. We prove an identity between
(1) The r-th central derivative of the quadratic base change L-function associated to an
everywhere unramified cuspidal automorphic representation π of PGL2;
(2) The self-intersection number of the π-isotypic component of the Heegner–Drinfeld cycle. This identity can be viewed as a function-field analog of the Waldspurger and Gross–Zagier formula for higher derivatives of L-functions.

http://arxiv.org/abs/1512.02683