On a theorem of Rickards

Håvard Damm-Johnsen

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arXiv · 2510.26655

On a theorem of Rickards

Håvard Damm-Johnsen

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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.

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Håvard Damm-Johnsen. 2025-10-30. On a theorem of Rickards. https://arxiv.org/abs/2510.26655

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