On a theorem of Rickards
Number Theory
2025-10-31 v1
Abstract
A recent result of Rickards states that the generating series of intersection numbers of real quadratic geodesics on indefinite Shimura curves are elliptic modular forms. We reinterpret this as a Kudla-Millson theta series, and prove that Rickards' generating series is the diagonal restriction of a Hilbert modular form, analogous to results of Darmon-Pozzi-Vonk and Branchereau.
Cite
@article{arxiv.2510.26655,
title = {On a theorem of Rickards},
author = {Håvard Damm-Johnsen},
journal= {arXiv preprint arXiv:2510.26655},
year = {2025}
}
Comments
20 pages, comments welcome!