Scholarly Communications Project

Document Type:Dissertation
Name:Frank Seaton Taylor
Email address:prime@vt.edu
URN:1997/00542
Title:Quintic Abelian Fields
Degree:Doctor of Philosophy
Department:Mathematics
Committee Chair: Charles J. Parry
Chair's email:parrycj@math.vt.edu
Committee Members:Joseph A. Ball
Ezra A. Brown
William J. Floyd
Lee W. Johnson
Keywords:Abelian Fields, Class Number, Conductor, Fundamental Unit, Quintic Fields
Date of defense:December 17, 1997
Availability:Release the entire work for Virginia Tech access only.
After one year release worldwide only with written permission of the student and the advisory committee chair.

Abstract:

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.

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