A note on the power residue symbol (Q2710119)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the power residue symbol |
scientific article |
Statements
19 April 2001
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quadratic reciprocity
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quartic reciprocity
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A note on the power residue symbol (English)
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In [Am. Math. Mon. 97, 138-139 (1990; Zbl 0748.11003)], \textit{R. G. Swan} gave a proof of the quadratic reciprocity law by expressing the Legendre symbol \((p/q)\) in terms of norms of certain units in cyclotomic extensions of \(\mathbb Q\). In this paper, the author examines to which degree Swan's approach generalizes to reciprocity laws of higher powers.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00053].
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