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 | English |
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Pages (from-to) | 117-194 |
Number of pages | 78 |
Journal | Advances in Mathematics |
Volume | 351 |
DOIs | |
State | Published - 31 Jul 2019 |
Externally published | Yes |
Keywords
- Gross–Zagier formula
- L-functions
- Waldspurger formula
All Science Journal Classification (ASJC) codes
- General Mathematics