## Abstract

Let F be the field of rational functions on a smooth projective curve over a finite field, and let π be an unramified cuspidal automorphic representation for PGL _{2} over F. We prove a variant of the formula of Yun and Zhang relating derivatives of the L-function of π to the self-intersections of Heegner-Drinfeld cycles on moduli spaces of shtukas. In our variant, instead of a self-intersection, we compute the intersection pairing of Heegner-Drinfeld cycles coming from two different quadratic extensions of F, and relate the intersection to the r-th derivative of a product of two toric period integrals.

Original language | American English |
---|---|

Pages (from-to) | 117-194 |

Number of pages | 78 |

Journal | Advances in Mathematics |

Volume | 351 |

DOIs | |

State | Published - 31 Jul 2019 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2019 Elsevier Inc.

## Keywords

- Gross–Zagier formula
- L-functions
- Waldspurger formula