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

Calculation of the first factor of the class number of the cyclotomic field


Author: Tauno Metsänkylä
Journal: Math. Comp. 23 (1969), 533-537
MSC: Primary 65.25; Secondary 10.00
MathSciNet review: 0247738
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Abstract | References | Similar Articles | Additional Information

Abstract: The values of the first factor $ {H_1}(m)$ of the class number of the $ m$th cyclotomic field are tabulated for 120 composite $ m$'s larger than 100. A conjecture concerning a divisibility property of $ {H_1}(m)$ is stated.


References [Enhancements On Off] (What's this?)

  • [1] Helmut Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (German). MR 0049239 (14,141a)
  • [2] E. Kummer, "Über die Klassenanzahl der aus $ n$ten Einheitswurzeln gebildeten komplexen Zahlen," Monatsh. Preuss. Akad. Wiss. Berlin, 1861, pp. 1051-1053.
  • [3] E. Kummer, "Über diejenigen Primzahlen $ \lambda $, für welche die Klassenzahl der aus $ \lambda $ten Einheitswurzeln gebildeten komplexen Zahlen durch $ \lambda $ theilbar ist," Monaish. Preuss. Akad. Wiss. Berlin, 1874, pp. 239-248.
  • [4] Timo Lepistö, On the first factor of the class number of the cyclotomic field and Dirichlet’s 𝐿-functions, Ann. Acad. Sci. Fenn. Ser. A I No. 387 (1966), 53. MR 0195843 (33 #4041)
  • [5] Tauno Metsänkylä, Über den ersten Faktor der Klassenzahl des Kreiskörpers, Ann. Acad. Sci. Fenn. Ser. A I No. 416 (1967), 48 (German). MR 0228466 (37 #4046)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0247738-8
PII: S 0025-5718(1969)0247738-8
Article copyright: © Copyright 1969 American Mathematical Society