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An upper bound for the index of χ-irregularity

Published online by Cambridge University Press:  26 February 2010

R. Ernvall
R. Ernvall
Affiliation:
Department of Mathematics, University of Turku, SF-20500 Turku, Finland.
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Extract

In the middle of the last century, Kummer's studies on the famous Fermat conjecture led him to the question: when does a given prime p > 2 divide the class number of the p-th cyclotomic field? His conclusion was that this happens, if, and only if, p divides at least one of the Bernoulli numbers B2, B4,…, Bp_3. Such a prime is called irregular. Carlitz [1] has given the simplest proof of the fact that the number of irregular primes is infinite. However, it is not known whether there are infinitely many regular primes.

Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 39 - 44
Copyright
Copyright © University College London 1985

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References

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