On a Conjecture of Yui and Zagier

TL;DR

This paper proves Yui and Zagier's conjecture on the factorization of resultants of minimal polynomials of Weber class invariants by expressing Weber function differences as Borcherds products.

Contribution

It introduces a novel method of expressing Weber function differences as Borcherds products to prove the conjecture.

Findings

Confirmed the factorization conjecture for Weber class invariants

Established a systematic approach using Borcherds products

Enhanced understanding of Weber function differences

Abstract

In this paper, 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.