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A Sequence of Results on Class Number Congruences

Published online by Cambridge University Press:  20 November 2018

Antone Costa
Antone Costa*
Affiliation:
Department of Mathematics The American University 4400 Massachusetts Avenue NW Washington D.C 20016 U.S.A.
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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.

Keywords

11R11
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 139 - 143
Copyright
Copyright © Canadian Mathematical Society 1993

References

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