Quadratic Reciprocity in a Finite Group

DOI10.2307/30037441zbMath1125.20003arXivmath/0311453OpenAlexW2950946844MaRDI QIDQ5703714

Kimberly Spears Hopkins, William Duke

Publication date: 8 November 2005

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311453

zbMATH Keywords

finite groupscharacter tablesLegendre symbolKronecker symbolDirichlet charactersquadratic reciprocitynumbers of real conjugacy classescharacters of Abelian groupsnumbers of complex conjugacy classes

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Power residues, reciprocity (11A15)

Related Items (13)

Epipelagic \(L\)-packets and rectifying characters ⋮ Permutations involving squares in finite fields ⋮ Class product and character product. ⋮ On some determinants with Legendre symbol entries ⋮ Jacobsthal sums and permutations of biquadratic residues ⋮ Quadratic residues and related permutations ⋮ The surveyability of long proofs ⋮ Yet another proof of the quadratic reciprocity law ⋮ Some identities for the partition function ⋮ 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 ⋮ POWER MAP PERMUTATIONS AND SYMMETRIC DIFFERENCES IN FINITE GROUPS ⋮ Extending the Zolotarev-Frobenius approach to quadratic reciprocity

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