An Extension of the Jacobi Symbol Due to Gauss Original Research Article

In a posthumous paper of Gauss the definition of the (nowadays called) Jacobi symbol for biquadratic residues in image(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 nth power residues in any suitable number field.