Résultats quantitatifs en approximation diophantienne

Schlickewei, Hans Peter

Journées arithmétiques de Luminy 17-21 Juillet 1989, Astérisque, no. 198-199-200 (1991), pp. 319-331.

[1] E. Bombieri et A. J. Van Der Poorten, Some quantitative results related to Roth's Theorem. J. Austral. Math. Soc. (Series A) 45 (1988), 233-248. | DOI | Zbl

E. Bombieri et A. J. Van Der Poorten, Some quantitative results related to Roth's Theorem. Corrigenda 48 (1990), 154-155. | Zbl

[2] J. Bourgain, The Riesz-Raikov Theorem for algebraic numbers, à paraître. | Zbl

[3] H. Davenport et K. F. Roth, Rational approximation to algebraic numbers, Mathematika 2 (1955), 160-167. | DOI | Zbl

[4] E. Dubois et G. Rhin, Sur la majoration de formes linéaires à coefficients algébriques réels et p-adiques; Démonstration d'une conjecture de K. Mahler, Cr. hebd. Séanc. Acad. Sci. Paris A 282 (1976), 1211-1214. | Zbl

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

[6] J. H. Evertse, On sums of $S$-units and linear recurrences, Compositio Math. 53 (1984), 225-244. | EuDML | Numdam | Zbl

[7] J. H. Evertse et K. Györy, On the numbers of solutions of weighted unit equations, Compositio Math. 66 (1988), 329-354. | EuDML | Numdam | Zbl

[8] H. Luckhardt, Herbrand-Analysen zweier Beweise des Satzes von Roth: polynomiale Anzahlschranken, Journ. of Symb. Logic. 54 (1989), 234-263. | DOI | Zbl

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

[10] A. J. Van Der Poorten et H. P. Schlickewei, The growth conditions for recurrence sequences, Macquarie Math. Reports, No. 82-0041, 1982.

[11] A. J. Van Der Poorten et H. P. Schlickewei, A diophantine problem in harmonic analysis, à paraître dans Math. Proc. Camb. Phil. Soc. | Zbl

[12] K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20. | DOI | Zbl

[13] H. P. Schlickewei, Linearformen mit algebraischen Koeffizienten, Manuscripta Math. 18 (1976), 147-185. | DOI | EuDML | Zbl

[14] H. P. Schlickewei, The $p$-adic Thue-Siegel-Roth-Schmidt theorem, Arch. Math. 29 (1977), 267-270. | DOI | Zbl

[15] H. P. Schlickewei, The number of subspaces occurring in the $p$-adic subspace theorem in diophantine approximation, Journ. Reine Angew. Math 406 (1990), 44-108. | EuDML | Zbl

[16] H. P. Schlickewei, An explicit upper bound for the number of solutions of the $S$-unit equaiton, Journ. Reine Angew. Math. 406 (1990), 109-120. | EuDML | Zbl

[17] H. P. Schlickewei, Linear equations in integers with bounded sum of digits, à paraître dans Journ. of Number Theory. | Zbl

[18] H. P. Schlickewei, The quantitative subspace theorem for number fields, soumis pour publication. | Numdam | Zbl

[19] H. P. Schlickewei, $S$-unit equations over number fields, à paraître dans Inventiones Math. | EuDML | Zbl

[20] W. M. Schmidt, Norm form equations, Annals of Math. 96 (1972), 526-551. | DOI | Zbl

[21] W. M. Schmidt, Simultaneous approximation to algebraic numbers by elements of a number field, Monatsh. Math. 79 (1975), 55-66. | DOI | EuDML | Zbl

[22] W. M. Schmidt, The subspace theorem in diophantine approximations, Compositio Math. 69 (1989), 121-173. | EuDML | Numdam | Zbl

[23] H. G. Senge et E. G. Straus, PV-numbers and sets of multiplicity, Per. Math. Hung. 3 (1973), 93-100. | DOI | Zbl

[24] C. L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuß. Akad. Wiss., Phys.-math. Kl. No. 1, 70 pp. (1929). | JFM

[25] J. H. Silverman, Lower bounds for height functions, Duke Math. Journ. 51 (1984), 395-403. | DOI | Zbl