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The First Factor of the Class Number of a Cyclic Field

Published online by Cambridge University Press:  20 November 2018

Leonard Carlitz
Leonard Carlitz*
Affiliation:
Duke University
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Extract

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Let p be a fixed prime > 3. The first factor of the field R(ζ), where R is the rational field and , is determined by means of

1.1,

where

r is a primitive root (mod p), and ri is the least positive residue of ri (mod p).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 23 - 26
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Beeger, N. G. W. H., Over de deelichamen van het cirkellichaam der lh-de machtswortels nit de eenlneid en hunne klassenaantallen (lste gedeelte), Konink. Akad. Wet. Amsterdam, 27 (1918), 324–336.Google Scholar
2. Beeger, N. G. W. H. , Over de deelichamen van het cirkellichaam der lh-de machtswortels uit de eenheid en hunne klassenaantallen (3de gedeelte), Konink. Akad. Wet. Amsterdam, 27 (1918), 822–827.Google Scholar
3. Nielsen, N., Traité élémentaire des nombres de Bernoulli (Paris, 1924).Google Scholar
4. Vandiver, H. S., On the first factor of the class number of a cyclotomic field, Bull. Amer. Math. Soc, 05(1918-19), 458–461.Google Scholar