Stickelberger subideals related to Kummer type congruences

Takashi Agoh

Mathematica Slovaca (1998)

  • Volume: 48, Issue: 4, page 347-364
  • ISSN: 0139-9918

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Agoh, Takashi. "Stickelberger subideals related to Kummer type congruences." Mathematica Slovaca 48.4 (1998): 347-364. <http://eudml.org/doc/31905>.

@article{Agoh1998,
author = {Agoh, Takashi},
journal = {Mathematica Slovaca},
keywords = {Stickelberger ideal; Kummer system of congruences; class number formula; cyclotomic field; Bernoulli number; Mirimanoff polynomial},
language = {eng},
number = {4},
pages = {347-364},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Stickelberger subideals related to Kummer type congruences},
url = {http://eudml.org/doc/31905},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Agoh, Takashi
TI - Stickelberger subideals related to Kummer type congruences
JO - Mathematica Slovaca
PY - 1998
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 48
IS - 4
SP - 347
EP - 364
LA - eng
KW - Stickelberger ideal; Kummer system of congruences; class number formula; cyclotomic field; Bernoulli number; Mirimanoff polynomial
UR - http://eudml.org/doc/31905
ER -

References

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  2. AGOH T., Some variations and consequences of the Kummer-Mirimanoff congruences, Acta Arith. 62 (1992), 73-96. (1992) Zbl0738.11031MR1179011
  3. AGOH T.-MORI K., Kummer type system of congruences and bases of Stickelberger subideals, Arch. Math. (Brno) 32 (1996), 211-232. (1996) Zbl0903.11007MR1421857
  4. AGOH T.-SKULA L., Kummer type congruences and Stickelberger subideals, Acta Arith. 75 (1996), 235-250. (1996) Zbl0841.11012MR1387862
  5. BENNETON G., Sur le dernier théoréme de Fermat, Ann. Sci. Univ. Besancon Math. 3 (1974). (1974) Zbl0348.10010MR0419347
  6. FUETER R., Kummers Kriterium zum letzten Theorem von Fermat, Math. Ann. 85 (1922), 11-20. (1922) MR1512040
  7. GRANVILLE A., Diophantine Equations with Varying Exponents (with Special Reference to FermaVs Last Theorem), Ph.D. Thesis, Queen's Univ., 1989. (1989) 
  8. HAZAMA F., Demjanenko matrix, class number, and Hodge group, J. Number Theory 34 (1990), 174-177. (1990) Zbl0697.12003MR1042490
  9. IWASAWA K., A class number formula for cyclotomic fields, Ann. of Math. 76 (1962), 171-179. (1962) Zbl0125.02003MR0154862
  10. KUMMER E. E., Einige Sätze über die aus den Wurzeln der Gleichung a λ = 1 gebildeten complexen Zahlen, für den Fall, dafl die Klassenanzahl durch λ teilbar 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]. 
  11. RIBENBOIM P., 13 Lectures on Fermat's Last Theorem, Springer-Verlag, New York, 1979. (1979) Zbl0456.10006MR0551363
  12. SINNOTT W., On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. (1980) Zbl0465.12001MR0595586
  13. SKULA L., A remark on Mirimanoff polynomials, Comment. Math. Univ. Sancti Pauli (Tokyo) 31 (1982), 89-97. (1982) Zbl0496.10006MR0674586
  14. SKULA L., Some bases of the Stickelberger ideal, Math. Slovaca 43 (1993), 541-571. (1993) Zbl0798.11044MR1273710
  15. SKULA L., On a special ideal contained in the Stickelberger ideal, J. Number Theory 58 (1996), 173-195. (1996) Zbl0861.11063MR1387734
  16. WASHINGTON L. C., Introduction to Cyclotomic Fields, Springer-Verlag, New York, 1982. (1982) Zbl0484.12001MR0718674

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