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.References
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Additional Information
- Noriko Yui
- Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
- MR Author ID: 186000
- Email: yui@ny.mast.queensu.ca
- Don Zagier
- Affiliation: Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, 53225 Bonn, Germany
- MR Author ID: 186205
- Email: zagier@mpim-bonn.mpg.de
- Received by editor(s): June 8, 1994
- Received by editor(s) in revised form: June 19, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 1645-1662
- MSC (1991): Primary 11G15; Secondary 11R37, 11F03, 11G16
- DOI: https://doi.org/10.1090/S0025-5718-97-00854-5
- MathSciNet review: 1415803