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An Extension of the Jacobi Symbol Due to Gauss

✍ Scribed by Detlef Gröger

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
136 KB
Volume
88
Category
Article
ISSN
0022-314X

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✦ Synopsis

In a posthumous paper of Gauss the definition of the (nowadays called) Jacobi symbol for biquadratic residues in Q(i) is based on a generalisation of the Gauss lemma and at the same time extended to all denominators prime to the numerator. We show what kind of characters result from an analogous extension of the Jacobi symbol for n th power residues in any suitable number field.

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