Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l

Stanislav Jakubec

Acta Arithmetica (1996)

  • Volume: 74, Issue: 4, page 293-310
  • ISSN: 0065-1036

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Stanislav Jakubec. "Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l." Acta Arithmetica 74.4 (1996): 293-310. <http://eudml.org/doc/206854>.

@article{StanislavJakubec1996,
author = {Stanislav Jakubec},
journal = {Acta Arithmetica},
keywords = {cyclic fields of prime degree; abelian extensions; cyclotomic units; Bernoulli numbers; class number},
language = {eng},
number = {4},
pages = {293-310},
title = {Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l},
url = {http://eudml.org/doc/206854},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Stanislav Jakubec
TI - Congruence of Ankeny-Artin-Chowla type modulo p² for cyclic fields of prime degree l
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 4
SP - 293
EP - 310
LA - eng
KW - cyclic fields of prime degree; abelian extensions; cyclotomic units; Bernoulli numbers; class number
UR - http://eudml.org/doc/206854
ER -

References

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  1. [1] K. Q. Feng, The Ankeny-Artin-Chowla formula for cubic cyclic number fields, J. China Univ. Sci. Tech. 12 (1982), 20-27. 
  2. [2] S. Jakubec, The congruence for Gauss period, J. Number Theory 48 (1994), 36-45. Zbl0807.11049
  3. [3] S. Jakubec, On divisibility of class number of real Abelian fields of prime conductor, Abh. Math. Sem. Univ. Hamburg 63 (1993), 67-86. Zbl0788.11052
  4. [4] S. Jakubec, On Vandiver's conjecture, Abh. Math. Sem. Univ. Hamburg 64 (1994), 105-124. Zbl0828.11059
  5. [5] S. Jakubec, Congruence of Ankeny-Artin-Chowla type for cyclic fields of prime degree l, Math. Proc. Cambridge Philos. Soc., to appear. Zbl0853.11086
  6. [6] A. A. Kiselev and I. Sh. Slavutskiĭ, The transformation of Dirichlet's formulas and the arithmetical computation of the class number of quadratic fields, in: Proc. Fourth All-Union Math. Congr. (Leningrad 1961), Vol. II, Nauka, Leningrad, 1964, 105-112 (in Russian). 
  7. [7] F. Marko, On the existence of p-units and Minkowski units in totally real cyclic fields, Abh. Math. Sem. Univ. Hamburg, to appear. Zbl0869.11087
  8. [8] R. Schertz, Über die analytische Klassenzahlformel für reelle abelsche Zahlkörper, J. Reine Angew. Math. 307/308 (1979), 424-430. 
  9. [9] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. Zbl0465.12001
  10. [10] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, in: Séminaire de Théorie des Nombres, Paris 1979-80, M.-J. Bertin (ed.), Progr. Math. 12, Birkhäuser, 1981, 277-286. 

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