Septic fields with discriminant ±2a3b

John W. Jones; David P. Roberts

doi:10.1090/S0025-5718-03-01510-2

Septic fields with discriminant ±2^a3^b

John W. Jones, David P. Roberts

Mathematics (Morris)

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

10 Scopus citations

Abstract

We classify septic number fields which are unramified outside of {∞, 2, 3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S₇. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.

Original language	English (US)
Pages (from-to)	1975-1985
Number of pages	11
Journal	Mathematics of Computation
Volume	72
Issue number	244
DOIs	https://doi.org/10.1090/S0025-5718-03-01510-2
State	Published - Oct 2003

Publisher link

10.1090/S0025-5718-03-01510-2

Find It

Find It at U of M Libraries

Cite this

@article{9f636f61901849bd9639c77d82171468,

title = "Septic fields with discriminant ±2a3b",

abstract = "We classify septic number fields which are unramified outside of {∞, 2, 3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S7. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.",

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

year = "2003",

month = oct,

doi = "10.1090/S0025-5718-03-01510-2",

language = "English (US)",

volume = "72",

pages = "1975--1985",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "244",

}

TY - JOUR

T1 - Septic fields with discriminant ±2a3b

AU - Jones, John W.

AU - Roberts, David P.

PY - 2003/10

Y1 - 2003/10

N2 - We classify septic number fields which are unramified outside of {∞, 2, 3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S7. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.

AB - We classify septic number fields which are unramified outside of {∞, 2, 3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S7. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.

UR - http://www.scopus.com/inward/record.url?scp=0141872525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141872525&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-03-01510-2

DO - 10.1090/S0025-5718-03-01510-2

M3 - Article

AN - SCOPUS:0141872525

SN - 0025-5718

VL - 72

SP - 1975

EP - 1985

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 244

ER -

Septic fields with discriminant ±2^a3^b

Abstract

Publisher link

Find It

Other files and links

Fingerprint

Cite this