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A Sequence of Results on Class Number Congruences
Published online by Cambridge University Press: 20 November 2018
Abstract
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Let p ≡ 1 mod 8 be a rational prime and let h(—p) be the class number of 
. In [1], Barrucand and Cohn show that h(-p) = 0 mod 8 iff p = x2 + 32y2 for some x,y € Z. In this article, we generalize their result to a family of relative quadratic extensions K/F, where Fk is the maximum totally real subfield of Q(ζ2k+2 ), and 
a power of a prime of Fk from a family of positive density.
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- Research Article
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- Copyright © Canadian Mathematical Society 1993
References
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