Type of Document Dissertation Author Taylor, Frank Seaton Author's Email Address email@example.com 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
- Fundamental Unit
- Quintic Fields
Date of Defense 1997-12-17 Availability unrestricted AbstractQuintic 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
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