A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles

Benjamin Howard, Ari Shnidman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageAmerican English
Pages (from-to)117-194
Number of pages78
JournalAdvances in Mathematics
Volume351
DOIs
StatePublished - 31 Jul 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

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

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