arXiv:2609.36463v2
Moments of the Cross-Sectional Siegel-Veech Transfrom
math.DS11H6037A1711B57
This arXiv record has been withdrawn. It duplicates arXiv:2609.33788, which is the canonical record.
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.
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Not a correctness certificate. A green “no issues found” result may include yellow suspected typos or minor formal issues that do not affect substantive soundness. It means this audit found no unresolved substantive error under the stated criteria; it does not replace expert scrutiny or formal verification.
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