|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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