Communications Project

Document Type:Dissertation
Name:Frank Seaton Taylor
Title:Quintic Abelian Fields
Degree:Doctor of Philosophy
Committee Chair: Charles J. Parry
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.


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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