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On a conjecture of Yui and Zagier. (English) Zbl 1469.11190

Summary: We prove the conjecture of Yui and Zagier concerning the factorization of the resultants of minimal polynomials of Weber class invariants. The novelty of our approach is to systematically express differences of certain Weber functions as products of Borcherds products.

MSC:

11G15 Complex multiplication and moduli of abelian varieties
11G18 Arithmetic aspects of modular and Shimura varieties
11F03 Modular and automorphic functions
11F27 Theta series; Weil representation; theta correspondences
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References:

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