The least admissible value of the parameter in Hilbert's Irreducibility Theorem

Andrzej Schinzel; Umberto Zannier

Acta Arithmetica (1995)

  • Volume: 69, Issue: 3, page 293-302
  • ISSN: 0065-1036

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Andrzej Schinzel, and Umberto Zannier. "The least admissible value of the parameter in Hilbert's Irreducibility Theorem." Acta Arithmetica 69.3 (1995): 293-302. <http://eudml.org/doc/206689>.

@article{AndrzejSchinzel1995,
author = {Andrzej Schinzel, Umberto Zannier},
journal = {Acta Arithmetica},
keywords = {estimate; irreducible polynomials; Hilbert's irreducibility theorem},
language = {eng},
number = {3},
pages = {293-302},
title = {The least admissible value of the parameter in Hilbert's Irreducibility Theorem},
url = {http://eudml.org/doc/206689},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Andrzej Schinzel
AU - Umberto Zannier
TI - The least admissible value of the parameter in Hilbert's Irreducibility Theorem
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 3
SP - 293
EP - 302
LA - eng
KW - estimate; irreducible polynomials; Hilbert's irreducibility theorem
UR - http://eudml.org/doc/206689
ER -

References

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  3. [De1] P. Dèbes, Parties hilbertiennes et progressions géométriques, C. R. Acad. Sci. Paris Sér. I 302 (1986), 87-90. Zbl0589.12001
  4. [De2] P. Dèbes, Hilbert subsets and s-integral points, preprint 1993, to appear. 
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  6. [Ei] M. Eichler, Zum Hilbertschen Irreduzibilitätssatz, Math. Ann. 116 (1939), 742-748. Zbl0021.00705
  7. [Fo] E. Fogels, On the abstract theory of primes III, Acta Arith. 11 (1966), 293-331. Zbl0142.01401
  8. [Fr] M. Fried, On Hilbert's irreducibility theorem, J. Number Theory 6 (1974), 211-231. Zbl0299.12002
  9. [Ha] H. Hasse, Number Theory, Springer, 1980. 
  10. [H] D. Hilbert, Ueber die Irreducibilität ganzer rationaler Functionen mit ganzzahligen Coefficienten, J. Reine Angew. Math. 110 (1892), 104-129 = Gesammelte Abhandlungen, Bd. II, Springer, 1970, 264-286. Zbl24.0087.03
  11. [In] E. Inaba, Über den Hilbertschen Irreduzibilitätssatz, Japan. J. Math. 19 (1944), 1-25. Zbl0060.04703
  12. [La] E. Landau, Sur quelques théorèmes de M. Petrovich relatifs aux zéros des fonctions analytiques, Bull. Soc. Math. France 33 (1905), 1-11. 
  13. [Me] F. Mertens, Über die Zerfällung einer ganzen Funktion einer Veränderlichen in zwei Faktoren, Sitzungsber. K. Akad. Wiss. Wien 120 (1911), Math. Naturwiss. Cl., 1485-1502. Zbl42.0114.04
  14. [Ro] P. Roquette, Nonstandard aspects of Hilbert's Irreducibility Theorem, in: Model Theory and Algebra (A memorial tribute to Abraham Robinson), Lecture Notes in Math. 498, Springer, 1975, 231-275. 
  15. [Sch] A. Schinzel, Selected Topics on Polynomials, The University of Michigan Press, Ann Arbor, 1982. 
  16. [Si] C. L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Phys. Math. Klasse 1929, Nr. 1 = Gesammelte Abhandlungen, Bd. I, Springer, 1966, 209-266. Zbl56.0180.05
  17. [Sk] T. Skolem, Untersuchungen über die möglichen Verteilungen ganzzahliger Lösungen gewisser Gleichungen, Kristiania Vid. Selskab. Skrifter I (1921), No. 17. Zbl48.0139.02
  18. [Spr] V. G. Sprindžuk, Diophantine equations involving unknown primes, Trudy Mat. Inst. Steklov. 158 (1981), 180-196 (in Russian). 
  19. [Ya] M. Yasumoto, Algebraic extensions of nonstandard models and Hilbert's irreducibility theorem, J. Symbolic Logic 53 (1988), 470-480. Zbl0657.03050

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