Vol. 14, No. 8, 2020

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On a conjecture of Yui and Zagier

Yingkun Li and Tonghai Yang

Vol. 14 (2020), No. 8, 2197–2238
DOI: 10.2140/ant.2020.14.2197
Abstract

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.

Keywords
modular form, Borcherds product, Weber invariants
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 11F03, 11F27
Milestones
Received: 17 December 2019
Accepted: 25 March 2020
Published: 18 September 2020
Authors
Yingkun Li
Technische Universität Darmstadt
Darmstadt
Germany
Tonghai Yang
University of Wisconsin, Madison
Madison, WI
United States