Fields containing values of algebraic functions

R. Dvornicich; U. Zannier

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 3, page 421-443
  • ISSN: 0391-173X

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Dvornicich, R., and Zannier, U.. "Fields containing values of algebraic functions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.3 (1994): 421-443. <http://eudml.org/doc/84186>.

@article{Dvornicich1994,
author = {Dvornicich, R., Zannier, U.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Hilbert's irreducibility theorem; irreducible polynomial; splitting field; discriminant},
language = {eng},
number = {3},
pages = {421-443},
publisher = {Scuola normale superiore},
title = {Fields containing values of algebraic functions},
url = {http://eudml.org/doc/84186},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Dvornicich, R.
AU - Zannier, U.
TI - Fields containing values of algebraic functions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 3
SP - 421
EP - 443
LA - eng
KW - Hilbert's irreducibility theorem; irreducible polynomial; splitting field; discriminant
UR - http://eudml.org/doc/84186
ER -

References

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  1. [1] E. Artin, Algebraic Numbers and Algebraic Functions. Gordon & Breach, New York (1967). Zbl0194.35301MR237460
  2. [2] A. Baker, Transcendental Number Theory. Cambridge Univ. Press, Cambridge (1976). Zbl0297.10013MR422171
  3. [3] Yu. Belotserkovski(Bilu), Effective analysis of a new class of Diophantine equations (Russian). Vestsī Akad. Navuk BSSR, Ser. Fīz.-Math. Navuk3 (1988), 111-115, (Math. Rev. 89i:11038). Zbl0649.10014MR958517
  4. [4] YU. Belotserkovski(Bilu), Effective analysis of a new class of Diophantine equations (Russian). Vestsī Akad. Navuk BSSR, Ser. Fiz.-Math. Navuk, 6 (1988), 34-39, (Math. Rev. 90j:11038). Zbl0669.10037MR984113
  5. [5] E. Bombieri, Le grand crible dans la théorie analitique des nombres. Astérisque 18, Societé Mathématique de France, Paris (1974). Zbl0292.10035MR371840
  6. [6] J.W.S. Cassels - A. Fröhlich, Algebraic Number Theory, Academic Press (1967). Zbl0153.07403MR215665
  7. [7] H. Davenport - J. Lewis - A. Schinzel, Polynomials of certain special types. Acta Arith.9 (1964), 107-116. Zbl0126.27801MR163880
  8. [8] P. Debes, Resultats recents liés au théorème d'irreductibilité de Hilbert. In: Séminaire de Théorie des Nombres, Paris 1985-86, Progress in Mathematics, vol. 71, Birkhauser. Zbl0632.12004
  9. [9] R. Dvornicich - U. Zannier, Fields containing values of algebraic functions. Preprint Univ. Pisa (Novembre 1983). Zbl0819.12003MR1310635
  10. [10] M. Fried, On Hilbert's Irreducibility Theorem, J. Number Theory6 (1974), 211-231. Zbl0299.12002MR349624
  11. [11] M. Fried - M. Jarden, Field Arithmetic. Springer-Verlag (1986). Zbl0625.12001MR868860
  12. [12] C. Hooley, Applications of sieve methods to the theory of numbers. Cambridge Tracts in Mathematics, Cambridge Univ. Press, 1976. Zbl0327.10044MR404173
  13. [13] S. Lang, Algebraic Number Theory. Addison Wesley (1970). Zbl0211.38404MR282947
  14. [14] S. Lang, Fundamentals of Diophantine Geometry. Springer-Verlag (1983). Zbl0528.14013MR715605
  15. [15] L.J. Mordell, Diophantine equations. Academic Press (1969). Zbl0188.34503MR249355
  16. [16] T. Nagell, Géneralisation d'un théorème de Tchebycheff. J. Math. Pures Appl.4 (1921), 243-356. Zbl48.1173.01JFM48.1173.01
  17. [17] A. Schinzel, Selected topics on polynomials. Univ. of Michigan Press, Ann Arbor (1982). Zbl0487.12002MR649775
  18. [18] J.P. Serre, Local fields. Springer-Verlag (1979). Zbl0423.12016MR554237
  19. [19] J.P. Serre, Lectures on the Mordell-Weil Theorem. Vieweg (1988). Zbl0863.14013MR1757192
  20. [20] A. Weil, Arithmetic on algebraic varieties. Annals of Math.53 (1951), 412-444. Zbl0043.27002MR42169
  21. [21] U. Zannier, Note on the effective solution of a certain diophantine problem. To appear. 

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