Document Type

Conference Proceeding

Publication Date

1999

Publication Title

CNTA-V: CRM Proceedings and Lecture Notes

Abstract

. Complete lists of number fields, of given degree n and unramified outside a given finite set S of primes, are both of intrinsic interest and useful in some applications. For degrees n ≤ 5 and S = {∞, 2, 3}, the complete lists have appeared previously; there are in total 85 such fields. Here we give the complete list for n = 6 and S = {∞, 2, 3}, finding in particular exactly 398 such fields. We use a three-pronged approach to obtain this classification: an exhaustive computer search, sextic twinning, and class field theory. Also we completely identify the 2-adic and 3-adic completions of all these degree ≤ 6 fields, this information being one of the focal points of interest and essential in applications

Volume

19

First Page

141

Last Page

172

Comments

First published in CNTA-V: CRM Proceedings and Lecture Notes 19 (1999), published by the American Mathematical Society and Centre de Recherches Mathématiques. © 1999 American Mathematical Society.

Rights

© 1999. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Included in

Number Theory Commons

Share

COinS