ON IDEAL CLASS GROUPS AND UNITS IN TERMS OF THE QUADRATIC FORM x2 + 32y2

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For quadratic number fields F = Q(√2pl … pt-1 ) with primes pj ≡ 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The results generalize nicely what has been familiar for the fields Q(√2p) with a prime p ≡ 1 mod 8, including density statements. And the results are stated in terms of the quadratic form x2 + 32y2 and illustrated in terms of graphs.
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