A SEQUENCE OF RESULTS ON CLASS NUMBER CONGRUENCES

Let p = 1 mod 8 be a rational prime and let h(-p) be the class number of Q(square-root p). In [1], Barrucand and Cohn show that h(-p) = 0 mod 8 iff p = x2 + 32y2 for some x, y is-an-element-of Z. In this article, we generalize their result to a family of relative quadratic extensions K/F, where F(k) is the maximum totally real subfield of Q(zeta2k+2), and K = F(k) (square-root -p(k), p(k) a power of a prime of F(k) from a family of positive density.