Elsevier

Journal of Number Theory

Volume 36, Issue 2, October 1990, Pages 145-159
Journal of Number Theory

The minimum discriminant of totally real octic fields

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Abstract

The minimum discriminant of totally real octic algebraic number fields is determined. It is 282,300,416 and belongs to the ray class field over Q(√2) of conductor (7 + 2 √2): F = Q(√α) for α = (7 + 2 √2 + (1 + √2) √7 + 2 √2)/2. There is—up to isomorphy—only one field of that discriminant. The next two smallest discriminant values are 309,593,125 and 324,000,000. For each field we present a full system of fundamental units and its class number.

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