A remark on elliptic units
type: Item
instance of: scholarly article
title: A remark on elliptic units
zbMATH Open document ID: 0716.11025
author: Akira Aiba
published in: Kodai Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: Let \(p\equiv 3(4)\) be a prime \(>3\) and let \(K={\mathbb{Q}}(\sqrt{-p})\). Let H be the absolute class field of K. In a paper published in 1982, \textit{B. H. Gross} [Prog. Math. 26, 219-236 (1982; Zbl 0506.14040)] defined units \(u_{\sigma}(\sigma \in Gal(H/K))\) in a class field of HT of a CM-field T containing K and asked a question regarding a property of these units. In the present paper, the author gives an explicit method of calculating \(u_{\sigma}\) following a result of \textit{G. Robert} [Ann. Sci. Ecole Norm. Sup., IV. Sér. 11, 297-389 (1978; Zbl 0409.12008)]. An interesting concrete example (the case \(p=23)\) is considered in detail at the end, where the answer to Gross' question is seen to be in the affirmative in this case.
Mathematics Subject Classification ID: 11G16
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 4179452
zbMATH Keywords: elliptic units
zbMATH Keywords: elliptic curves
zbMATH Keywords: class field
zbMATH Keywords: CM-field
reviewed by: A. R. Rajwade
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039157
OpenAlex ID: W2027817743
cites work: Arithmetic on elliptic curves with complex multiplication. II
cites work: Q5790213
cites work: Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
cites work: Q3328654
cites work: Q3953865
cites work: Q4075566
cites work: Nombres de Hurwitz et unités elliptiques. Un critère de régularité pour les extensions abéliennes d'un corps quadratique imaginaire
cites work: Minimal basis and inessential discriminant divisors for a cubic field
DOI: 10.2996/KMJ/1138039157
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description: scientific article; zbMATH DE number 4179452