Title page for ETD etd-111897-10412

Type of Document

Dissertation

Author

Taylor, Frank Seaton

Author's Email Address

prime@vt.edu

URN

etd-111897-10412

Title

Quintic Abelian Fields

Degree

Doctor of Philosophy

Department

Mathematics

Advisory Committee

Advisor Name	Title
Charles J. Parry	Committee Chair
Ezra A. Brown	Committee Member
Joseph A. Ball	Committee Member
Lee W. Johnson	Committee Member
William J. Floyd	Committee Member

Keywords

Abelian Fields
Class Number
Conductor
Fundamental Unit
Quintic Fields

Date of Defense

1997-12-17

Availability

restricted

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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