2019
DOI: 10.48550/arxiv.1909.04103
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Computing intersections of closed geodesics on the modular curve

James Rickards

Abstract: In a recent work of Duke, Imamoḡlu, and Tóth, the linking number of certain links on the space SL(2, Z)\ SL(2, R) is investigated. In this paper, we give an alternative interpretation of this linking number by relating it to the intersection number of modular geodesics on the modular curve. We demonstrate a connection to the results of Gross and Zagier on the factorization of differences of singular moduli by finding a real quadratic analogue of one of their results. By relating the intersection number to rive… Show more

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