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Abstract: Bruinier and Yang conjectured a formula for an intersection number on thearithmetic Hilbert modular surface, CMK.T m, where CMK is the zero-cycle ofpoints corresponding to abelian surfaces with CM by a primitive quartic CMfield K, and T m is the Hirzebruch-Zagier divisors parameterizing products ofelliptic curves with an m-isogeny between them. In this paper, we examinefields not covered by Yang-s proof of the conjecture. We give numericalevidence to support the conjecture and point to some interesting anomalies. Wecompare the conjecture to both the denominators of Igusa class polynomials andthe number of solutions to the embedding problem stated by Goren and Lauter.



Author: Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter, Adriana Salerno, Bianca Viray, Erika Wittenborn

Source: https://arxiv.org/







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