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ELEMENTS OF ORDER FOUR IN THE NARROW CLASS GROUP OF REAL QUADRATIC FIELDS

Published online by Cambridge University Press:  28 September 2015

ELLIOT BENJAMIN*
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA email ben496@prexar.com
C. SNYDER
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA email snyder@math.umaine.edu
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Abstract

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Using the elements of order four in the narrow ideal class group, we construct generators of the maximal elementary $2$-class group of real quadratic number fields with even discriminant which is a sum of two squares and with fundamental unit of positive norm. We then give a characterization of when two of these generators are equal in the narrow sense in terms of norms of Gaussian integers.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Cohen, H., A Course in Computational Algebraic Number Theory (Springer, New York, 1996).Google Scholar
Cohn, H., Advanced Number Theory (Dover, New York, 1980).Google Scholar
Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers, 4th edn (Oxford University Press, London, 1960).Google Scholar
Lemmermeyer, F., Reciprocity Laws (Springer, New York, 2000).CrossRefGoogle Scholar
Lemmermeyer, F., ‘Relations in the 2-class group of quadratic number fields’, J. Aust. Math. Soc. 93 (2012), 115120.CrossRefGoogle Scholar