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

Published online by Cambridge University Press:  20 March 2017

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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Extract

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2017 

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