Norm residue symbol and cyclotomic units

Charles Helou

Acta Arithmetica (1995)

  • Volume: 73, Issue: 2, page 147-188
  • ISSN: 0065-1036

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Charles Helou. "Norm residue symbol and cyclotomic units." Acta Arithmetica 73.2 (1995): 147-188. <http://eudml.org/doc/206815>.

@article{CharlesHelou1995,
author = {Charles Helou},
journal = {Acta Arithmetica},
keywords = {cyclotomic units; Hilbert's norm residue symbol; Fermat's Last Theorem; Artin-Hasse explicit reciprocity law},
language = {eng},
number = {2},
pages = {147-188},
title = {Norm residue symbol and cyclotomic units},
url = {http://eudml.org/doc/206815},
volume = {73},
year = {1995},
}

TY - JOUR
AU - Charles Helou
TI - Norm residue symbol and cyclotomic units
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 2
SP - 147
EP - 188
LA - eng
KW - cyclotomic units; Hilbert's norm residue symbol; Fermat's Last Theorem; Artin-Hasse explicit reciprocity law
UR - http://eudml.org/doc/206815
ER -

References

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  1. [1] N. Ankeny, E. Artin and S. Chowla, The class number of real quadratic number fields, Ann. of Math. 56 (1952), 479-493. Zbl0049.30605
  2. [2] E. Artin and J. Tate, Class Field Theory, Benjamin, New York, 1967. Zbl1179.11040
  3. [3] Z. Borevich and I. Shafarevich, Number Theory, Academic Press, London, 1966. 
  4. [4] P. G. L. Dirichlet, Recherches sur diverses applications de l'analyse infinitésimale à la théorie des nombres, J. Reine Angew. Math. 19 (1839), 324-369; 21 (1840), 1-12, 134-155. 
  5. [5] H. Hasse, Bericht über die neueren Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil II: Reziprozitätsgesetz, Jahresber. Deutsch. Math.-Verein., Leipzig, 1930. 
  6. [6] C. G. J. Jacobi, Über die Kreistheilung und ihre Anwendung auf die Zahlentheorie, Monatsh. Akad. Wiss. Berlin 1837, 127-136; also J. Reine Angew. Math. 30 (1846), 166-182. 
  7. [7] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Monograf. Mat. 57, PWN (Polish Scientific Publishers), Warszawa, 1974. Zbl0276.12002
  8. [8] J.-P. Serre, Corps Locaux, Hermann, Paris, 1968. 
  9. [9] G. Terjanian, Sur la loi de réciprocité des puissances l-èmes, Acta Arith. 54 (1989), 87-125. Zbl0642.12010
  10. [10] L. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982 Zbl0484.12001

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