Triviality of the l-class groups in Zp-extensions of Q(√-1) for split primes p ≡ 1 modulo 4

被引：0

作者：

Lamplugh, Jack ^{[1
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WA, England

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2014年 / 157卷 / 01期

关键词：

CLASS NUMBER; ELLIPTIC-CURVES;

D O I：

10.1017/S030500411400022X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the class numbers in the finite layers of certain non-cyclotomic Z(p)-extensions of the imaginary quadratic field Q(root-1), for all primes p equivalent to 1 modulo 4. By studying the Mahler measure of elliptic units, we are able to show that there are only finitely many primes l congruent to a primitive root modulo p(2) that divide any of the class numbers in the Z(p)-extension.

引用

页码：169 / 188

页数：20

共 3 条

[1] On the structure of order 4 class groups of Q(√n2+1)
Chakraborty, Kalyan
Hoque, Azizul
Mishra, Mohit
ANNALES MATHEMATIQUES DU QUEBEC, 2021, 45 (01): : 203 - 212
[2] A COMPUTABLE FORMULA FOR THE CLASS NUMBER OF THE IMAGINARY QUADRATIC FIELD Q(√-p), p=4n-1
Villeda, Jorge garcia
ELECTRONIC RESEARCH ARCHIVE, 2021, 29 (06): : 3853 - 3865
[3] On divisibility of the class number h+ of the real cyclotomic fields\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Q}(\zeta _p + \zeta _p^{1 - } )$$ \end{document} by primes q ≤5000by primes q ≤5000
S. Jakubec
P. Trojovský
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1997, 67 (1) : 269 - 280

← 1 →