On divisibility of the class number of real octic fields of a prime conductor p = n 4 + 16 by p

Stanislav Jakubec

Archivum Mathematicum (1994)

  • Volume: 030, Issue: 4, page 263-270
  • ISSN: 0044-8753

Abstract

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The aim of this paper is to prove the following Theorem Theorem Let K be an octic subfield of the field Q ( ζ p + ζ p - 1 ) and let p = n 4 + 16 be prime. Then p divides h K if and only if p divides B j for some j = p - 1 8 , 3 p - 1 8 , 5 p - 1 8 , 7 p - 1 8 .

How to cite

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Jakubec, Stanislav. "On divisibility of the class number of real octic fields of a prime conductor $p=n^4+16$ by $p$." Archivum Mathematicum 030.4 (1994): 263-270. <http://eudml.org/doc/247554>.

@article{Jakubec1994,
abstract = {The aim of this paper is to prove the following Theorem Theorem Let $K$ be an octic subfield of the field $Q(\zeta _p+\zeta _p^\{-1\})$ and let $p=n^4+16$ be prime. Then $p$ divides $h_K$ if and only if $p$ divides $B_j$ for some $j=\frac\{p-1\}\{8\}$, $3\frac\{p-1\}\{8\}$, $5\frac\{p-1\}\{8\}$, $7\frac\{p-1\}\{8\}$.},
author = {Jakubec, Stanislav},
journal = {Archivum Mathematicum},
keywords = {cyclotomic field; Bernoulli numbers},
language = {eng},
number = {4},
pages = {263-270},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On divisibility of the class number of real octic fields of a prime conductor $p=n^4+16$ by $p$},
url = {http://eudml.org/doc/247554},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Jakubec, Stanislav
TI - On divisibility of the class number of real octic fields of a prime conductor $p=n^4+16$ by $p$
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 4
SP - 263
EP - 270
AB - The aim of this paper is to prove the following Theorem Theorem Let $K$ be an octic subfield of the field $Q(\zeta _p+\zeta _p^{-1})$ and let $p=n^4+16$ be prime. Then $p$ divides $h_K$ if and only if $p$ divides $B_j$ for some $j=\frac{p-1}{8}$, $3\frac{p-1}{8}$, $5\frac{p-1}{8}$, $7\frac{p-1}{8}$.
LA - eng
KW - cyclotomic field; Bernoulli numbers
UR - http://eudml.org/doc/247554
ER -

References

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