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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Quintic polynomials and real cyclotomic fields with large class numbers


Authors: René Schoof and Lawrence C. Washington
Journal: Math. Comp. 50 (1988), 543-556
MSC: Primary 11R11; Secondary 11R16, 11R21, 11R27
MathSciNet review: 929552
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Abstract: We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime $ p = 641491$ the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an appendix we give a characterization of the "simplest" quadratic, cubic and quartic fields.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1988-0929552-2
PII: S 0025-5718(1988)0929552-2
Keywords: Cyclotomic fields, class number, unit group, geometry of numbers
Article copyright: © Copyright 1988 American Mathematical Society