Sur la norme du groupe des unités d'extensions quadratiques relatives

Georges Gras

Acta Arithmetica (1992)

  • Volume: 61, Issue: 4, page 307-317
  • ISSN: 0065-1036

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Georges Gras. "Sur la norme du groupe des unités d'extensions quadratiques relatives." Acta Arithmetica 61.4 (1992): 307-317. <http://eudml.org/doc/206468>.

@article{GeorgesGras1992,
author = {Georges Gras},
journal = {Acta Arithmetica},
keywords = {quadratic extension; group of units; norm map; 2-Sylow subgroups; class groups; fundamental unit},
language = {fre},
number = {4},
pages = {307-317},
title = {Sur la norme du groupe des unités d'extensions quadratiques relatives},
url = {http://eudml.org/doc/206468},
volume = {61},
year = {1992},
}

TY - JOUR
AU - Georges Gras
TI - Sur la norme du groupe des unités d'extensions quadratiques relatives
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 4
SP - 307
EP - 317
LA - fre
KW - quadratic extension; group of units; norm map; 2-Sylow subgroups; class groups; fundamental unit
UR - http://eudml.org/doc/206468
ER -

References

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  1. [C-H] P. Conner and J. Hurrelbrink, Class Number Parity, Ser. Pure Math. 8, World Sci., Singapore 1988. 
  2. [C-K] A. Costa and R. Kingan, On the norms of units for real quadratic extensions of number fields, preprint. 
  3. [F] A. Fröhlich, The generalization of a theorem of L. Rédei's, Quart. J. Math. Oxford Ser. (2) 5 (1954), 130-140. Zbl0058.26903
  4. G. Gras, Sur les l-classes d'idéaux dans les extensions cycliques relatives de degré premier l, Ann. Inst. Fourier (Grenoble) 23 (3) (1973), 1-48; 23 (4) (1973), 1-44. Zbl0276.12013
  5. [H] M. Hikita, On the congruences for the class numbers of the quadratic fields whose discriminants are divisible by 8, J. Number Theory 23 (1) (1986), 86-101. Zbl0587.12002
  6. [Hu] J. Hurrelbrink, On the norm of the fundamental unit, preprint. 
  7. [I] E. Inaba, Über die Struktur der l-Klassengruppe zyklischer Zahlkörper von Primzahlgrad l, J. Fac. Sci. Univ. Tokyo Sect. I 4 (1940), 61-115. Zbl0024.01002
  8. [M] P. Morton, On the non-existence of abelian conditions governing solvability of the -1 Pell equation, J. Reine Angew. Math. 405 (1990), 147-155. Zbl0689.12006
  9. [P] R. Pioui, Mesures de Haar p-adiques et interprétation arithmétique de (1/2)L₂(χ,s)-(1/2)L₂(χ,t), s,t ∈ ℤ₂ (χ quadratique), Thèse, Univ. Besançon, 1990. 
  10. [R1] L. Rédei, Arithmetischer Beweis des Satzes über die Anzahl der durch vier teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper, J. Reine Angew. Math. 171 (1934), 55-61. Zbl60.0125.02
  11. [R2] L. Rédei, Über die Grundeinheit und die durch acht teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper, J. Reine Angew. Math., 171 (1934), 131-148. Zbl0009.29302
  12. [S] A. Scholtz, Über die Lösbarkeit der Gleichung t²-Du²=-4, Math. Z. 39 (1934), 95-111. 

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