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On the Singular Values of Weber Modular Functions

Noriko Yui and Don Zagier
Mathematics of Computation
Vol. 66, No. 220 (Oct., 1997), pp. 1645-1662
Stable URL: http://www.jstor.org/stable/2153690
Page Count: 18
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Singular Values of Weber Modular Functions
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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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