Mixed degree number field computations

John Jones; David P. Roberts

doi:10.1007/s11139-018-0024-9

Mixed degree number field computations

John Jones, David P. Roberts

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

Abstract

We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL ₂(7 ) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2 ³: GL ₃(2 ) of smallest absolute discriminant.

Original language	English (US)
Pages (from-to)	47-66
Number of pages	20
Journal	Ramanujan Journal
Volume	47
Issue number	1
DOIs	https://doi.org/10.1007/s11139-018-0024-9
State	Published - Oct 1 2018

Keywords

Discriminant
Galois group
Number field
Ramification

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/s11139-018-0024-9

Cite this

@article{7e8ff5adf85e433f92b9b05f24d2c53b,

title = "Mixed degree number field computations",

abstract = "We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL 2(7 ) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2 3: GL 3(2 ) of smallest absolute discriminant.",

keywords = "Discriminant, Galois group, Number field, Ramification",

author = "John Jones and Roberts, {David P.}",

note = "Funding Information: Roberts{\textquoteright} contribution was partially supported by the Simons Foundation through grant #209472 and, in its final stages, by the National Science Foundation, through grant DMS-1601350. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2018",

month = oct,

day = "1",

doi = "10.1007/s11139-018-0024-9",

language = "English (US)",

volume = "47",

pages = "47--66",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Mixed degree number field computations

AU - Jones, John

AU - Roberts, David P.

N1 - Funding Information: Roberts’ contribution was partially supported by the Simons Foundation through grant #209472 and, in its final stages, by the National Science Foundation, through grant DMS-1601350. Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL 2(7 ) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2 3: GL 3(2 ) of smallest absolute discriminant.

AB - We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL 2(7 ) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2 3: GL 3(2 ) of smallest absolute discriminant.

KW - Discriminant

KW - Galois group

KW - Number field

KW - Ramification

UR - http://www.scopus.com/inward/record.url?scp=85049678510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049678510&partnerID=8YFLogxK

U2 - 10.1007/s11139-018-0024-9

DO - 10.1007/s11139-018-0024-9

M3 - Article

AN - SCOPUS:85049678510

SN - 1382-4090

VL - 47

SP - 47

EP - 66

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1

ER -

Mixed degree number field computations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this