On a conjecture of Yui and Zagier

Li, Yingkun; Yang, Tonghai

doi:10.2140/ant.2020.14.2197

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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.

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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

Vol. 14, No. 8, 2020