Year: 2026
Type: preprint
Abstract: We study the Siegel--Veech transform on the Poincaé section for the horocycle flow consisting of lattice surfaces with a visible horizontal holonomy vector of length at most one. We compute its first moment and derive formulas for higher and factorial moments. We emphasize these formulas in the case of the square torus of unit area and, as an application, use its first moment formula to recover the Boca--Zaharescu pair-correlation density for Farey fractions.
Source: arXiv (Cornell University)
Author: Artiles, Albert
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214734387