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Computing Polynomials of the Ramanujan tn Class Invariants

Published online by Cambridge University Press:  20 November 2018

Elisavet Konstantinou and
Aristides Kontogeorgis
Elisavet Konstantinou
Affiliation:
Department of Information and Communication Systems Engineering, University of the Aegean, 83200 Karlovassi, Samos, Greece e-mail: ekonstantinou@aegean.gr
Aristides Kontogeorgis
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece e-mail: kontogar@aegean.gr
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Abstract

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We compute the minimal polynomials of the Ramanujan values ${{t}_{n}}$ , where $n\,\equiv \,11\,\bmod \,24$ , using the Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field $\mathbb{Q}\left( \sqrt{-n} \right)$ and have much smaller coefficients than the Hilbert polynomials.

Keywords

11R2933E0511R20

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 4 , 01 December 2009, pp. 583 - 597
Copyright
Copyright © Canadian Mathematical Society 2009

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