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Construction of ray-class fields by smaller generators and their applications

Part of: Computational number theory Algebraic number theory: global fields Arithmetic algebraic geometry

Published online by Cambridge University Press:  20 March 2017

Ja Kyung Koo  and
Dong Sung Yoon
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea (jkkoo@math.kaist.ac.kr; math dsyoon@kaist.ac.kr)
Dong Sung Yoon
Affiliation:
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea (jkkoo@math.kaist.ac.kr; math dsyoon@kaist.ac.kr)
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We generate ray-class fields over imaginary quadratic fields in terms of Siegel–Ramachandra invariants, which are an extension of a result of Schertz. By making use of quotients of Siegel–Ramachandra invariants we also construct ray-class invariants over imaginary quadratic fields whose minimal polynomials have relatively small coefficients, from which we are able to solve certain quadratic Diophantine equations.

Keywords

class field theorymodular unitsDiophantine equations

MSC classification

Secondary: 11R37: Class field theory 11G16: Elliptic and modular units 11Y50: Computer solution of Diophantine equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 4 , August 2017 , pp. 781 - 812
Copyright
Copyright © Royal Society of Edinburgh 2017