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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.

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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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