Prime factors of cyclotomic class numbers

Lehmer, D. H.

doi:10.1090/S0025-5718-1977-0432589-6

Prime factors of cyclotomic class numbers

Author: D. H. Lehmer
Journal: Math. Comp. 31 (1977), 599-607
MSC: Primary 12A50; Secondary 12A35
DOI: https://doi.org/10.1090/S0025-5718-1977-0432589-6
MathSciNet review: 0432589
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Abstract: Let p be an odd prime. The "first factor" ${h^\ast }(p)$ of the class number of the field of pth roots of unity has been the subject of many investigations beginning with Kummer (1861). In the present paper it is shown how the theory of a function introduced by T. A. Pierce (1917) can be used to find the prime factors of ${h^\ast }(p)$.

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D. H. LEHMER & J. M. MASLEY, "Table of the cyclotomic class numbers ${h^\ast }(p)$ and their factors for $200 < p < 512$." (To appear.)