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On Russell-Type Modular Equations

Published online by Cambridge University Press:  20 November 2018

Heng Huat Chan  and
Wen-Chin Liaw
Heng Huat Chan
Affiliation:
Department of Mathematics, National Chung Cheng University, Minhsiung, Chiayi 621, Taiwan email: hhchan@mthmp.math.ccu.edu.tw
Wen-Chin Liaw
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA email: liaw@math.uiuc.edu
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Abstract

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In this paper, we revisit Russell-type modular equations, a collection of modular equations first studied systematically by R. Russell in 1887. We give a proof of Russell’s main theorem and indicate the relations between such equations and the constructions of Hilbert class fields of imaginary quadratic fields. Motivated by Russell’s theorem, we state and prove its cubic analogue which allows us to construct Russell-type modular equations in the theory of signature 3.

Keywords

33D1033C0511F11
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 1 , 01 February 2000 , pp. 31 - 46
Copyright
Copyright © Canadian Mathematical Society 2000

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