Some bases of the Stickelberger ideal

Ladislav Skula

Mathematica Slovaca (1993)

  • Volume: 43, Issue: 5, page 541-571
  • ISSN: 0139-9918

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Skula, Ladislav. "Some bases of the Stickelberger ideal." Mathematica Slovaca 43.5 (1993): 541-571. <http://eudml.org/doc/34366>.

@article{Skula1993,
author = {Skula, Ladislav},
journal = {Mathematica Slovaca},
keywords = {Stickelberger ideal; group ring; cyclotomic field; bases; Sinnott's formula; relative class number; index formula; Fermat equation; Kummer system; Bernoulli numbers; Mirimanoff polynomials},
language = {eng},
number = {5},
pages = {541-571},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Some bases of the Stickelberger ideal},
url = {http://eudml.org/doc/34366},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Skula, Ladislav
TI - Some bases of the Stickelberger ideal
JO - Mathematica Slovaca
PY - 1993
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 43
IS - 5
SP - 541
EP - 571
LA - eng
KW - Stickelberger ideal; group ring; cyclotomic field; bases; Sinnott's formula; relative class number; index formula; Fermat equation; Kummer system; Bernoulli numbers; Mirimanoff polynomials
UR - http://eudml.org/doc/34366
ER -

References

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  4. GRANVILLE A. J., Diophantine Equations with Varying Exponents (with Special Reference to Fermat's Last Theorem), Ph. D. thesis, Queen's University, 1987. (1987) 
  5. IWASAWA K., A class number formula for cyclotomic fields, Ann. of Math. 76 (1962), 171-179. (1962) Zbl0125.02003MR0154862
  6. KUČERA R., On bases of the Stickelberger ideal and of the group of circular units of a cyclotomic fields, J. Number Theory 40 (1992), 284-316. (1992) MR1154041
  7. KUMMER E. E., Über die Zerlegung der aus Wurzeln der Einheit gebildeten complexen Zahlen in ihre Primfactoren, J. Reine Angew. Math. 35 (1847), 327-367, (Coll. Papers I, 211-251). 
  8. KUMMER E. E., Einige Sëtze 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, Abh. Königl. Akad. Wiss., Berlin (1857), 41-74, (Coll. Papers I, 639-692). 
  9. LERCH M., Zur Theorie des Fermatschen Quotienten (a p-1 - 1)/p = q(a), Math. Ann. 60 (1905), 471-490. (1905) MR1511321
  10. LE LIDEC P., Sur une forme nouvelle des congruences de Kummer-Mirimanoff, C.R. Acad. Sci. Paris Sér. A 265 (1967), 89-90. (1967) Zbl0154.29602MR0217013
  11. LE LIDEC P., Nouvelle forme des congruences de Kummer-Mirimanoff pour le premier cas du théorème de Fermat, Bull. Soc. Math. France 97 (1969), 321-328. (1969) Zbl0188.10102MR0262158
  12. NEWMAN M., A table of the first factor for prime cyclotomic fields, Math. Comp. 24(109) (1970), 215-219. (1970) MR0257029
  13. SINNOTT W., On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. 108 (1978), 107-134. (1978) Zbl0395.12014MR0485778
  14. SINNOTT W., On the Stickelberger ideal and the circular units of an abelian field, In: Invent. Math. 62, Springer, Berlin-New York, 1980, pp. 181-234. (1980) Zbl0465.12001MR0595586
  15. SKULA L., Index of irregularity of a prime, J. Reine Angew. Math. 315 (1980), 92-106. (1980) Zbl0419.10016MR0564526
  16. SKULA L., Another proof of Iwasawa's class number formula, Acta Arith. XXXIX (1981), 1-6. (1981) Zbl0372.12012MR0638737
  17. SKULA L., A remark on Mirimanoff polynomials, Comment. Math. Univ. St. Paul. 31 (1982), 89-97. (1982) Zbl0496.10006MR0674586
  18. SKULA L., Systems of equations depending on certain ideals, Arch. Math. (Brno) 21 (1985), 23-38. (1985) Zbl0589.12005MR0818304
  19. SKULA L., A note on the index of irregularity, J. Number Theory 22 (1986), 125-138. (1986) Zbl0589.12006MR0826946
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  21. WASHINGTON L. C., Introduction to Cyclotomic Fields, Springer-Verlag, New York-Heidelberg-Berlin, 1982. (1982) Zbl0484.12001MR0718674

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