Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T06:26:01.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized irregular primes

Published online by Cambridge University Press:  26 February 2010

Reijo Ernvall
Reijo Ernvall
Affiliation:
Department of Mathematics, University of Turku, SF-20500 Turku, Finland
Get access

Extract

A prime p > 2 is called irregular, if it divides the numerator of at least one of the Bernoulli numbers B2, B4, …, Bp – 3 (in the even suffix notation). The study of irregular primes has its origin in the famous theorem of Kummer which states that p divides the class number of the p-th cyclotomic field, if, and only if, p is irregular. Carlitz [1] has given the simplest proof of the fact that the number of irregular primes is infinite.

Type
Research Article
Information
Mathematika , Volume 30 , Issue 1 , June 1983 , pp. 67 - 73
Copyright
Copyright © University College London 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Carlitz, L.. Note on irregular primes. Proc. Amer. Math. Soc, 5 (1954), 329–331.Google Scholar
2.Ernvall, R.. Generalized Bernoulli numbers, generalized irregular primes, and class number. Ann. Univ. Turku Ser. A Math., 178 (1979), 72 pp.Google Scholar
3.Iwasawa, K.. Lectures on p-adic L-functions (Princeton University Press, 1972).CrossRefGoogle Scholar
4.Leopoldt, H.-W.. Eine Verallgemeinerung der Bernoullischen Zahlen. Abh. Math. Sem. Univ. Hamburg, 22 (1958), 131–140.Google Scholar