An examination of class number for [reproduction of quadratic extensions] where [reproduction of square root of d] has continued fraction expansion of period three
- UNCW Author/Contributor (non-UNCW co-authors, if there are any, appear on document)
- Brent O. J. Young (Creator)
- Institution
- The University of North Carolina Wilmington (UNCW )
- Web Site: http://library.uncw.edu/
- Advisor
- Michael Freeze
Abstract: We begin by ¯nding an appropriate parametrization for d that will ensure pd has
continued fraction expansion of period three. After ¯nding this parametrization, we
use elementary arguments to limit the possible values of d leading to real quadratic
number ¯elds Q(pd) of class number one to a set of 30 congruence classes modulo
9240. We then examine the class number formula, and using an analytic result we
are able to place an upper bound on d beyond which the class number must exceed
one (with at most one exception).
We conclude by examining algorithms that enable us to compute the class num-
ber more e±ciently. Using such algorithms (as programmed in PARI) we give an
enumeration of all such ¯elds with class number one.
An examination of class number for [reproduction of quadratic extensions] where [reproduction of square root of d] has continued fraction expansion of period three
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Created on 1/1/2009
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Additional Information
- Publication
- Thesis
- A Thesis Submitted to University North Carolina Wilmington in Partial Ful¯llment Of the Requirements for the Degree of Master of Science
- Language: English
- Date: 2009
- Keywords
- Field extensions (Mathematics), Mathematical optimization
- Subjects
- Field extensions (Mathematics)
- Mathematical optimization