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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A simple proof of the Zolotareff-Frobenius theorem
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by Robert E. Dressler and Ernest E. Shult PDF
Proc. Amer. Math. Soc. 54 (1976), 53-54 Request permission

Abstract:

We give a noncomputational, elementary group-theoretic proof of the Zolotareff-Frobenius Theorem. We use no results from the theory of quadratic residues.
References
    G. Frobenius, Über das quadratische Reziprozitätsgesetz. I, S.-B. Preuss. Akad. Wiss. Berlin 1914, 335-349. M. Lerch, Sur un Théorème arithmétique de Zolotarev, Bull. Intern. 3, Prague, 1896.
  • C. Meyer, Über einige Anwendungen Dedekindscher Summen, J. Reine Angew. Math. 198 (1957), 143–203 (German). MR 104643, DOI 10.1515/crll.1957.198.143
  • Marcel Riesz, Sur le lemme de Zolotareff et sur la loi de réciprocité des restes quadratiques, Math. Scand. 1 (1953), 159–169 (French). MR 57273, DOI 10.7146/math.scand.a-10376
    • E. Zolotareff, Nouvelle démonstration de la loi de réciprocité de Legendre, Novelles Ann. Math. (2) 11 (1872), 355-362.
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 54 (1976), 53-54
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0389732-8
  • MathSciNet review: 0389732