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Mathematics of Computation

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On the singular values of Weber modular functions

Authors: Noriko Yui and Don Zagier
Journal: Math. Comp. 66 (1997), 1645-1662
MSC (1991): Primary 11G15; Secondary 11R37, 11F03, 11G16
MathSciNet review: 1415803
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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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Additional Information

Noriko Yui
Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
MR Author ID: 186000

Don Zagier
Affiliation: Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, 53225 Bonn, Germany
MR Author ID: 186205

Received by editor(s): June 8, 1994
Received by editor(s) in revised form: June 19, 1996
Article copyright: © Copyright 1997 American Mathematical Society