Linking numbers and non-holomorphic Siegel modular forms
Number Theory
2025-04-22 v2 Differential Geometry
Geometric Topology
Abstract
We study generating series encoding linking numbers between geodesics in arithmetic hyperbolic -folds. We show that the series converge to functions on genus Siegel space and that certain explicit modifications have the transformation properties of genus Siegel modular forms of weight . This is done by carefully analyzing the integral of the Kudla--Millson theta series over a Seifert surface with geodesic boundary. As a corollary, we deduce a polynomial bound on the linking numbers.
Cite
@article{arxiv.2410.17231,
title = {Linking numbers and non-holomorphic Siegel modular forms},
author = {Mads Bjerge Christensen},
journal= {arXiv preprint arXiv:2410.17231},
year = {2025}
}
Comments
Added a new theorem, fixed various typos, and improved the exposition. 46 pages, 2 figures