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1. Introduetion In an earlier paper in this Journal [1], the authors developed special properties of primes p = χ + 32?/, perhaps the most interesting of which is the fact that h( — ip), the class number of (£)()/ — /?), is divisible by 8. It would therefore be of some interest t o find the 8-class-field of < (|/ — p} but, unfortunately, this seems too difficult. Nevertheless, some ray class-fields over QQ/ — p) and ty(\/ — 2/>), with conductors of norm 32, are still of interest because of their relation to the rational theory of quadratic forms and to the diophantine equation 4F + l = /?Γ, (see Theorems 5.1 and 8.1 below, in particular.)

On some class-fields related to primes of type x2 + 32y2.