Quintic Abelian Fields

Quintic abelian fields are characterized in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class group structure is not immediate from the class number, six have their structure computed.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1997

Author dc:creator

• Taylor, Frank Seaton

Chair dc:contributor.committeechair

• Parry, Charles J.

Committee members dc:contributor.committeemember

• Floyd, William J.
• Johnson, Lee W.
• Brown, Ezra A.
• Ball, Joseph A.

• Abelian Fields
• Class Number
• Conductor
• Fundamental Unit
• Quintic Fields

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-111897-10412

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/29662