Kummer type congruences and Stickelberger subideals

Takashi Agoh; Ladislav Skula

Acta Arithmetica (1996)

  • Volume: 75, Issue: 3, page 235-250
  • ISSN: 0065-1036

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Takashi Agoh, and Ladislav Skula. "Kummer type congruences and Stickelberger subideals." Acta Arithmetica 75.3 (1996): 235-250. <http://eudml.org/doc/206874>.

@article{TakashiAgoh1996,
author = {Takashi Agoh, Ladislav Skula},
journal = {Acta Arithmetica},
keywords = {Kummer system of congruences; first case of Fermat's last theorem; Bernoulli numbers; Mirimanoff polynomials; Stickelberger ideal; cyclotomic field; modified Demjanenko matrix},
language = {eng},
number = {3},
pages = {235-250},
title = {Kummer type congruences and Stickelberger subideals},
url = {http://eudml.org/doc/206874},
volume = {75},
year = {1996},
}

TY - JOUR
AU - Takashi Agoh
AU - Ladislav Skula
TI - Kummer type congruences and Stickelberger subideals
JO - Acta Arithmetica
PY - 1996
VL - 75
IS - 3
SP - 235
EP - 250
LA - eng
KW - Kummer system of congruences; first case of Fermat's last theorem; Bernoulli numbers; Mirimanoff polynomials; Stickelberger ideal; cyclotomic field; modified Demjanenko matrix
UR - http://eudml.org/doc/206874
ER -

References

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  1. [1] T. Agoh, On the criteria of Wieferich and Mirimanoff, C. R. Math. Rep. Acad. Sci. Canada 8 (1986), 49-52. Zbl0585.10009
  2. [2] T. Agoh, On the Kummer-Mirimanoff congruences, Acta Arith. 55 (1990), 141-156. Zbl0648.10013
  3. [3] T. Agoh, Some variations and consequences of the Kummer-Mirimanoff congruences, Acta Arith. 62 (1992), 73-96. Zbl0738.11031
  4. [4] G. Benneton, Sur le dernier théorème de Fermat, Ann. Sci. Univ. Besançon Math. 3 (1974), 15pp. 
  5. [5] P. J. Davis, Circulant Matrices, Wiley, New York, 1979. Zbl0418.15017
  6. [6] H. G. Folz and H. G. Zimmer, What is the rank of the Demjanenko matrix?, J. Symbolic Comput. 4 (1987), 53-67. Zbl0624.14001
  7. [7] R. Fueter, Kummers Kriterium zum letzten Theorem von Fermat, Math. Ann. 85 (1922), 11-20. Zbl48.0130.05
  8. [8] F. Hazama, Demjanenko matrix, class number, and Hodge group, J. Number Theory 34 (1990), 174-177. Zbl0697.12003
  9. [9] F. Hazama, Hodge cycles on the Jacobian variety of the Catalan curve, preprint, 1994. 
  10. [10] K. Iwasawa, A class number formula for cyclotomic fields, Ann. of Math. 76 (1962), 171-179. Zbl0125.02003
  11. [11] E. E. Kummer, Einige Sätze über die aus den Wurzeln der Gleichung α λ = 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. [12] M. Lerch, Zur Theorie des Fermatschen Quotienten ( a p - 1 - 1 ) / p = q ( a ) , Math. Ann. 60 (1905), 471-490. Zbl36.0266.03
  13. [13] P. Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer, New York, 1979. 
  14. [14] J. W. Sands and W. Schwarz, A Demjanenko matrix for abelian fields of prime power conductor, J. Number Theory 52 (1995), 85-97. Zbl0829.11054
  15. [15] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. Zbl0465.12001
  16. [16] L. Skula, A remark on Mirimanoff polynomials, Comment. Math. Univ. St. Paul. (Tokyo) 31 (1982), 89-97. Zbl0496.10006
  17. [17] L. Skula, Some bases of the Stickelberger ideal, Math. Slovaca 43 (1993), 541-571. Zbl0798.11044
  18. [18] L. Skula, On a special ideal contained in the Stickelberger ideal, J. Number Theory, to appear. Zbl0861.11063

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