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Index for subgroups of the group of units in number fields

Tsutomu Shimada (1998)

Acta Arithmetica

We define a sequence of rational integers u i ( E ) for each finite index subgroup E of the group of units in some finite Galois number fields K in which prime p ramifies. For two subgroups E’ ⊂ E of finite index in the group of units of K we prove the formula v p ( [ E : E ' ] ) = i = 1 r u i ( E ' ) - u i ( E ) . This is a generalization of results of P. Dénes [3], [4] and F. Kurihara [5].

Jacobi symbols, ambiguous ideals, and continued fractions

R. A. Mollin (1998)

Acta Arithmetica

The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.

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