On the singular values of Weber modular functions

Yui, Noriko; Zagier, Don

doi:10.1090/S0025-5718-97-00854-5

On the singular values of Weber modular functions
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by Noriko Yui and Don Zagier PDF

Math. Comp. 66 (1997), 1645-1662 Request permission

Abstract:

The minimal polynomials of the singular values of the classical Weber modular functions give far simpler defining polynomials for the class fields of imaginary quadratic fields than the minimal polynomials of singular moduli of level 1. We describe computations of these polynomials and give conjectural formulas describing the prime decomposition of their resultants and discriminants, extending the formulas of Gross-Zagier for the level 1 case.

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