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On the relation between units and Jacobi sums in prime cyclotomic fields

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References

  1. Artin, E. and Tate, J.: Class Field Theory. New York: Benjamin 1967

    Google Scholar 

  2. Dickson, L. E.: Cyclotomy, higher congruences, and Waring's problem. Amer. J. Math. 57, 391–424 (1935)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hasse, H.: Beritch über neuere Untersuchungen und Probleme aus der Teorie der algebraischen Zahlkörper. Teil II: Reziprozitätsgesetz. Würzburg-Vienna: Pysica-Verlag 1965

    Google Scholar 

  4. Kummer, E.: Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetsen, J. reine angew. Math 44, 93–146 (1852). Collected Papers, I, 485–538.

    Google Scholar 

  5. Lang. S.: Algebraic Number Theory, Addison-Wesley 1970

  6. Lang, S.: Cyclotomic Fields I and II, Combined Second Edition. New York: Springer-Verlag 1990

    MATH  Google Scholar 

  7. Niven I. and Zuckerman H.S.: An Introduction to the Theory of Numbers. New York: John Wiley 1960

    MATH  Google Scholar 

  8. Pollaczec Felix: Relations entre les derivées logarithmiques de Kummer at les logarithmes π-adiques, Bull. Sci. Math. (2) 70, 199–218 (1946)

    MATH  MathSciNet  Google Scholar 

  9. Rademacher, H.: Topics in Analytic Number Theory. Berlin: Springer-Verlag 1973

    MATH  Google Scholar 

  10. Washington, L.C.: Introduction to Cyclotomic Fields, Graduate Texts in Mathematics. New York: Springer-Verlag 1982

    Google Scholar 

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This research was partially done at The Institute for Advanced Study where the author held a fellowship of the John Simon Guggenheim Memorial Foundation, at McGill University and Concordia University.

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Thaine, F. On the relation between units and Jacobi sums in prime cyclotomic fields. Manuscripta Math 73, 127–151 (1991). https://doi.org/10.1007/BF02567634

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  • DOI: https://doi.org/10.1007/BF02567634

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