The least admissible value of the parameter in Hilbert's Irreducibility Theorem
Andrzej Schinzel ; Umberto Zannier
Acta Arithmetica, Tome 69 (1995), p. 293-302 / Harvested from The Polish Digital Mathematics Library
Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:206689
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     author = {Andrzej Schinzel and Umberto Zannier},
     title = {The least admissible value of the parameter in Hilbert's Irreducibility Theorem},
     journal = {Acta Arithmetica},
     volume = {69},
     year = {1995},
     pages = {293-302},
     zbl = {0828.12003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav69i3p293bwm}
}
Andrzej Schinzel; Umberto Zannier. The least admissible value of the parameter in Hilbert's Irreducibility Theorem. Acta Arithmetica, Tome 69 (1995) pp. 293-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav69i3p293bwm/

[000] [BP] E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), 337-357. | Zbl 0718.11048

[001] [Co] S. D. Cohen, The distribution of Galois groups and Hilbert's irreducibility theorem, Proc. London Math. Soc. (3) 43 (1981), 227-250. | Zbl 0484.12002

[002] [De1] P. Dèbes, Parties hilbertiennes et progressions géométriques, C. R. Acad. Sci. Paris Sér. I 302 (1986), 87-90. | Zbl 0589.12001

[003] [De2] P. Dèbes, Hilbert subsets and s-integral points, preprint 1993, to appear.

[004] [Do] K. Dörge, Einfacher Beweis des Hilbertschen Irreduzibilitätssatzes, Math. Ann. 96 (1927), 176-182. | Zbl 52.0101.01

[005] [Ei] M. Eichler, Zum Hilbertschen Irreduzibilitätssatz, Math. Ann. 116 (1939), 742-748. | Zbl 0021.00705

[006] [Fo] E. Fogels, On the abstract theory of primes III, Acta Arith. 11 (1966), 293-331. | Zbl 0142.01401

[007] [Fr] M. Fried, On Hilbert's irreducibility theorem, J. Number Theory 6 (1974), 211-231. | Zbl 0299.12002

[008] [Ha] H. Hasse, Number Theory, Springer, 1980.

[009] [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. | Zbl 24.0087.03

[010] [In] E. Inaba, Über den Hilbertschen Irreduzibilitätssatz, Japan. J. Math. 19 (1944), 1-25. | Zbl 0060.04703

[011] [La] E. Landau, Sur quelques théorèmes de M. Petrovich relatifs aux zéros des fonctions analytiques, Bull. Soc. Math. France 33 (1905), 1-11.

[012] [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. | Zbl 42.0114.04

[013] [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.

[014] [Sch] A. Schinzel, Selected Topics on Polynomials, The University of Michigan Press, Ann Arbor, 1982.

[015] [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. | Zbl 56.0180.05

[016] [Sk] T. Skolem, Untersuchungen über die möglichen Verteilungen ganzzahliger Lösungen gewisser Gleichungen, Kristiania Vid. Selskab. Skrifter I (1921), No. 17. | Zbl 48.0139.02

[017] [Spr] V. G. Sprindžuk, Diophantine equations involving unknown primes, Trudy Mat. Inst. Steklov. 158 (1981), 180-196 (in Russian).

[018] [Ya] M. Yasumoto, Algebraic extensions of nonstandard models and Hilbert's irreducibility theorem, J. Symbolic Logic 53 (1988), 470-480. | Zbl 0657.03050