ArticleOriginal scientific text

Title

Kummer type congruences and Stickelberger subideals

Authors 1, 2

Affiliations

  1. Department of Mathematics, Science University of Tokyo, Noda, Chiba 278, Japan
  2. Department of Mathematics, Faculty of Science, Masaryk University, 662 95 Brno, Czech Republic

Bibliography

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  2. T. Agoh, On the Kummer-Mirimanoff congruences, Acta Arith. 55 (1990), 141-156.
  3. T. Agoh, Some variations and consequences of the Kummer-Mirimanoff congruences, Acta Arith. 62 (1992), 73-96.
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  5. P. J. Davis, Circulant Matrices, Wiley, New York, 1979.
  6. H. G. Folz and H. G. Zimmer, What is the rank of the Demjanenko matrix?, J. Symbolic Comput. 4 (1987), 53-67.
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  8. F. Hazama, Demjanenko matrix, class number, and Hodge group, J. Number Theory 34 (1990), 174-177.
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  10. K. Iwasawa, A class number formula for cyclotomic fields, Ann. of Math. 76 (1962), 171-179.
  11. E. E. Kummer, Einige Sätze über die aus den Wurzeln der Gleichung αλ=1 gebildeten complexen Zahlen, für den Fall, daß die Klassenanzahl durch λ theilbar ist, nebst Anwendung derselben auf einen weiteren Beweis des letzten Fermat'schen Lehrsatzes, Abhandl. Königl. Akad. Wiss. Berlin 1857, 41-74; Collected Papers, Vol. I, 639-692.
  12. M. Lerch, Zur Theorie des Fermatschen Quotienten ap-1-1p=q(a), Math. Ann. 60 (1905), 471-490.
  13. P. Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer, New York, 1979.
  14. J. W. Sands and W. Schwarz, A Demjanenko matrix for abelian fields of prime power conductor, J. Number Theory 52 (1995), 85-97.
  15. W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234.
  16. L. Skula, A remark on Mirimanoff polynomials, Comment. Math. Univ. St. Paul. (Tokyo) 31 (1982), 89-97.
  17. L. Skula, Some bases of the Stickelberger ideal, Math. Slovaca 43 (1993), 541-571.
  18. L. Skula, On a special ideal contained in the Stickelberger ideal, J. Number Theory, to appear.
Pages:
235-250
Main language of publication
English
Received
1995-05-05
Accepted
1995-10-31
Published
1996
Exact and natural sciences