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 PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Parry, Charles J. Committee Chair
Ball, Joseph A. Committee Member
Brown, Ezra A. Committee Member
Floyd, William J. Committee Member
Johnson, Lee W. Committee Member
Keywords
  • Abelian Fields
  • Class Number
  • Conductor
  • Fundamental Unit
  • Quintic Fields
Date of Defense 1997-12-17
Availability unrestricted
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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