On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree
Helmut Locher
Acta Arithmetica, Tome 89 (1999), p. 97-122 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207264
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     author = {Helmut Locher},
     title = {On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {97-122},
     zbl = {0938.11035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav89i2p97bwm}
}
Helmut Locher. On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree. Acta Arithmetica, Tome 89 (1999) pp. 97-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav89i2p97bwm/

[000] [1] Bombieri, E. and van der Poorten, A. J.: Some quantitative results related to Roth's Theorem, Macquarie Math. Reports, Report No. 87-0005, February 1987. | Zbl 0664.10017

[001] [2] Bombieri, E. and Vaaler, J.: On Siegel's Lemma, Invent. Math. 73 (1983), 11-32. | Zbl 0533.10030

[002] [3] Davenport, H. and Roth, K. F.: Rational approximations to algebraic numbers, Mathematika 2 (1955), 160-167. | Zbl 0066.29302

[003] [4] Esnault, H. and Viehweg, E.: Dyson's Lemma for polynomials in several variables (and the Theorem of Roth), Invent. Math. 78 (1984), 445-490. | Zbl 0545.10021

[004] [5] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584. | Zbl 0521.10015

[005] [6] J.-H. Evertse, An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma, Acta Arith. 73 (1995), 215-248. | Zbl 0857.11034

[006] [7] J.-H. Evertse, An improvement of the quantitative Subspace theorem, Compositio Math. 101 (1996), 225-311. | Zbl 0856.11030

[007] [8] J.-H. Evertse, The number of algebraic numbers of given degree approximating a given algebraic number, in: Analytic Number Theory, Y. Motohashi (ed.), London Math. Soc. Lecture Notes Ser. 247, Cambridge Univ. Press, 1998, 53-83. | Zbl 0919.11048

[008] [9] Faltings, G.: Diophantine approximation on abelian varieties, Ann. of Math. 133 (1991), 549-576. | Zbl 0734.14007

[009] [10] Luckhardt, H.: Herbrand-Analysen zweier Beweise des Satzes von Roth: polynomiale Anzahlschranken, J. Symbolic Logic 54 (1989), 234-263. | Zbl 0669.03024

[010] [11] Mahler, K.: Zur Approximation algebraischer Zahlen I. (Über den größten Primteiler binärer Formen), Math. Ann. 107 (1933), 691-730. | Zbl 0006.10502

[011] [12] Mueller, J. and Schmidt, W. M.: On the number of good rational approximations to algebraic numbers, Proc. Amer. Math. Soc. 106 (1987), 859-866. | Zbl 0675.10023

[012] [13] Roth, K. F.: Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20. | Zbl 0064.28501

[013] [14] Schlickewei, H. P.: The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273. | Zbl 0751.11033

[014] [15] Schmidt, W. M.: Simultaneous approximation to algebraic numbers by rationals, Acta Math. 125 (1970), 189-201. | Zbl 0205.06702

[015] [16] Schmidt, Diophantine Approximations, Lecture Notes in Math. 785, Springer, 1980. | Zbl 0432.10029

[016] [17] Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, 1991.

[017] [18] Stolarsky, K. B.: Algebraic Numbers and Diophantine Approximation, Dekker, 1974. | Zbl 0285.10022

[018] [19] Wirsing, E.: On approximations of algebraic numbers by algebraic numbers of bounded degree, in: Number Theory Institute 1969, Proc. Sympos. Pure Math. 20, Amer. Math. Soc., 1971, 213-247