Extending the Zolotarev-Frobenius approach to quadratic reciprocity

DOI10.1007/s11139-014-9635-yzbMath1395.11013OpenAlexW2045026873MaRDI QIDQ2345879

Adrian Brunyate, Pete L. Clark

Publication date: 21 May 2015

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-014-9635-y

zbMATH Keywords

signatureJacobi symbolquadratic reciprocityabstract number ringfinite principal ringZolotarev permutation

Mathematics Subject Classification ID

Principal ideal rings (13F10) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Power residues, reciprocity (11A15)

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Some permutations over \(\mathbb{F}_p\) concerning primitive roots ⋮ Warning's second theorem with relaxed outputs ⋮ CUBES IN FINITE FIELDS AND RELATED PERMUTATIONS ⋮ Permutations involving squares in finite fields ⋮ On some determinants with Legendre symbol entries ⋮ Unnamed Item ⋮ Generalization of a Result of Sylvester Regarding the Frobenius Coin Problem and an Elementary Proof of Eisenstein's Lemma for Jacobi Symbols ⋮ Quadratic residues and related permutations and identities ⋮ APPLICATIONS OF LERCH’S THEOREM TO PERMUTATIONS OF QUADRATIC RESIDUES

Uses Software

• MathOverflow
• PlanetMath

Cites Work

• A new property of the Jacobi symbol
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• A note on Euclidean order types
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• Über kommutative Ringe, in denen jedes Ideal als Produkt von Primidealen darstellbar ist
• POWER MAP PERMUTATIONS AND SYMMETRIC DIFFERENCES IN FINITE GROUPS
• A Generalization of Zolotarev's Theorem
• A Simple Proof of the Zolotareff-Frobenius Theorem
• The Characters of linear permutations
• On Characterizations of Prüfer Rings.
• Two Criteria for Dedekind Domains
• Quadratic Reciprocity in a Finite Group
• Sur le lemme de Zolotareff et sur la loi de réciprocité des restes quadratiques
• On the Commutator Subgroup of the General Linear Group
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