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Number Theory Related to Fermat’s Last Theorem pp 31–43Cite as

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Kummer, Eisenstein, and Higher Reciprocity Laws

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Part of the book series: Progress in Mathematics ((PM,volume 26))

Abstract

This lecture might almost have been called “Kummer versus Eisenstein” and higher reciprocity laws, because its subject is the rivalry between these two men and how it contributed to the development of the higher reciprocity laws. However, the word “versus” suggests an antagonism and unfriendliness which, with one mild exception, does not appear to have been a feature of their rivalry.

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References

  1. Edwards, H.M., “The Background of Kummer’s Proof of Fermat’s Last Theorem for Regular Primes,” Arch. Hist. Exact Sei. 14 (1975), 219–236.

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  2. Edwards, H.M., “Postscript to ‘The Background of Kummer’s Proof...’,” Aroh. Eist. Exaot Sei. 17 (1977), 381–394.

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  3. Eisenstein, G., “Über ein einfaches Mittel zur Auffindung der höheren Reciprocitätsgesetze und der mit ihnen zu verbindenden Ergänzungssätze,” J. für Math. (Crelle) 39 (1850), 351–364 (Werke, vol. 2, 623–636.

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  4. Eisenstein, G., “Beweis der allgemeinsten Reciprocitätsgesetze zwischen reellen und komplexen Zahlen,” Monatsber. Akad. Wiss. Berlin, 1850, 189–198 (Werke, vol. 2, 712–721.

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  5. Kummer, E.E., “Allgemeine Reciprocitätsgesetze für beliebig hohe Potenzreste,” Monatsber. Akad. Wiss. Berlin, 1850, 154–165 (Collected Pccpers, vol. 1, 35–357 ).

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  6. Kummer, E.E., “Über die Ergänzungssatze zu den allgemeinen Reciprocitätsgesetzen,” J. für Math. (Crelle) 44 (1852), 93–146 (Collected Papers, vol. 1, 485–146 ).

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Author information

Authors and Affiliations

  1. Tables photographs courtesy of STAATSBIBLIOTHEK, Handschriftenabteilung, Postfach 1407, 1000, Berlin 30, Germany

    Harold M. Edwards

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  1. Harold M. Edwards
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Washington, GN-50, 98195, Seattle, WA, USA

    Neal Koblitz

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© 1982 Springer Science+Business Media New York

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Edwards, H.M. (1982). Kummer, Eisenstein, and Higher Reciprocity Laws. In: Koblitz, N. (eds) Number Theory Related to Fermat’s Last Theorem. Progress in Mathematics, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6699-5_2

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  • DOI: https://doi.org/10.1007/978-1-4899-6699-5_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3104-8

  • Online ISBN: 978-1-4899-6699-5

  • eBook Packages: Springer Book Archive

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