@incollection{AST_2008__317__1_0, author = {Bilu, Yuri F.}, title = {The many faces of the subspace theorem [after {Adamczewski,} {Bugeaud,} {Corvaja,} {Zannier...]}}, booktitle = {S\'eminaire Bourbaki - Volume 2006/2007 - Expos\'es 967-981}, series = {Ast\'erisque}, note = {talk:967}, pages = {1--38}, publisher = {Soci\'et\'e math\'ematique de France}, number = {317}, year = {2008}, mrnumber = {2487729}, zbl = {1220.11091}, language = {en}, url = {http://www.numdam.org/item/AST_2008__317__1_0/} }
TY - CHAP AU - Bilu, Yuri F. TI - The many faces of the subspace theorem [after Adamczewski, Bugeaud, Corvaja, Zannier...] BT - Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981 AU - Collectif T3 - Astérisque N1 - talk:967 PY - 2008 SP - 1 EP - 38 IS - 317 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2008__317__1_0/ LA - en ID - AST_2008__317__1_0 ER -
%0 Book Section %A Bilu, Yuri F. %T The many faces of the subspace theorem [after Adamczewski, Bugeaud, Corvaja, Zannier...] %B Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981 %A Collectif %S Astérisque %Z talk:967 %D 2008 %P 1-38 %N 317 %I Société mathématique de France %U http://www.numdam.org/item/AST_2008__317__1_0/ %G en %F AST_2008__317__1_0
Bilu, Yuri F. The many faces of the subspace theorem [after Adamczewski, Bugeaud, Corvaja, Zannier...], dans Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 967, 38 p. http://www.numdam.org/item/AST_2008__317__1_0/
[1] On the complexity of algebraic numbers. II. Continued fractions", Acta Math. 195 (2005), p. 1-20. | DOI | MR | Zbl
& - "[2] On the complexity of algebraic numbers. I. Expansions in integer bases", Ann. of Math. (2) 165 (2007), p. 547-565. | DOI | MR | Zbl
& , "[3] On the Maillet-Baker continued fractions", J. reine angew. Math. 606 (2007), p. 105-121. | MR | Zbl
& , "[4] Sur la complexité des nombres algébriques", C. R. Math. Acad. Sci. Paris 339 (2004), p. 11-14. | DOI | MR | Zbl
, & - "[5] Automatic sequences. Theory, applications, generalizations, Cambridge University Press, 2003. | MR | Zbl
& -[6] Diophantine approximation, Lectures from the C.I.M.E. Summer School held in Cetraro, June 28-July 6, 2000. Lecture Notes in Mathematics 1819, Springer, 2003. | MR | Zbl
& (eds.) -[7] Géométrie des surfaces algébriques et points entiers", arXiv:math.NT/0606184. | Numdam | MR
- "[8] A note on universal Hilbert sets", J. reine angew. Math. 479 (1996), p. 195-203. | EuDML | MR | Zbl
- "[9] Heights in Diophantine geometry, New Mathematical Monographs, vol. 4, Cambridge University Press, 2006. | MR | Zbl
& -[10] Les probabilités dénombrables et leurs applications arithmétiques", Palermo Rend. 27 (1909), p. 247-271. | DOI | JFM
- "[11] Sur les chiffres décimaux de et divers problèmes de probabilités en chaîne", C. R. Acad. Sci. Paris 230 (1950), p. 591-593. | MR | Zbl
, "[12] An upper bound for the G.C.D. of and ", Math. Z. 243 (2003), p. 79-84. | DOI | MR | Zbl
, & - "[13] A quantitative lower bound for the greatest prime factor of ", Acta Arith. 114 (2004), p. 275-294. | DOI | MR | Zbl
& - "[14] On the period of the continued fraction expansion of ", Indag. Math. N.S. 16 (2005), p. 21-35. | DOI | MR | Zbl
, "[15] Zur Transzendenz gewisser Reihen", Monatsh. Math. 104 (1987), p. 199-223. | DOI | EuDML | MR | Zbl
& - "[16] On the Hartmanis-Stearns problem for a class of tag machines", in IEEE Conference Record of 1968 Ninth Annual Symposium on Switching and Automata Theory, Schenectady, 1968, p. 51-60.
- "[17] Uniform tag sequences", Math. Systems Theory 6 (1972), p. 164-192. | DOI | MR | Zbl
, "[18] A lower bound for periods of matrices", Comm. Math. Phys. 252 (2004), p. 535-541. | DOI | MR | Zbl
, & - "[19] Diophantine equations with power sums and universal Hilbert sets", Indag. Math. (N.S.) 9 (1998), p. 317-332. | DOI | MR | Zbl
& - "[20] Finiteness of integral values for the ratio of two linear recurrences", Invent. Math. 149 (2002), p. 431-451. | DOI | MR | Zbl
& , "[21] Some new applications of the subspace theorem", Compositio Math. 131 (2002), p. 319-340. | DOI | MR | Zbl
& , "[22] A subspace theorem approach to integral points on curves", C. R. Math. Acad. Sci. Paris 334 (2002), p. 267-271. | DOI | MR | Zbl
& , "[23] On the greatest prime factor of ", Proc. Amer. Math. Soc. 131 (2003), p. 1705-1709. | DOI | MR | Zbl
& , "[24] On the number of integral points on algebraic curves", J. reine angew. Math. 565 (2003), p. 27-42. | MR | Zbl
& , "[25] On a general Thue's equation", Amer. J. Math. 126 (2004), p. 1033-1055. | DOI | MR | Zbl
& , "[26] On integral points on surfaces", Ann. of Math. (2) 160 (2004), p. 705-726. | DOI | MR | Zbl
& , "[27] On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France", Acta Math. 193 (2004), p. 175-191. | DOI | MR | Zbl
& , "[28] A lower bound for the height of a rational function at S-unit points", Monatsh. Math. 144 (2005), p. 203-224. | DOI | MR | Zbl
& , "[29] On the length of the continued fraction for values of quotients of power sums", J. Théor. Nombres Bordeaux 17 (2005), p. 737-748. | DOI | EuDML | Numdam | MR | Zbl
& , "[30] -unit points on analytic hypersurfaces", Ann. Sci. École Norm. Sup. (4) 38 (2005), p. 76-92. | DOI | EuDML | Numdam | MR | Zbl
& , "[31] On the integral points on certain surfaces", Int. Math. Res. Not. (2006), Art. ID 98623. | MR | Zbl
& , "[32] Universal Hilbert subsets", Math. Proc. Cambridge Philos. Soc. 124 (1998), p. 127-134. | DOI | MR | Zbl
& - "[33] The absolute subspace theorem and linear equations with unknowns from a multiplicative group", in Number theory in progress, Vol. 1 (Zakopane-Kościelisko, 1997, de Gruyter, 1999, p. 121-142. | MR | Zbl
& - "[34] A quantitative version of the absolute subspace theorem", J. reine angew. Math. 548 (2002), p. 21-127. | MR | Zbl
& , "[35] Diophantine approximation on abelian varieties", Ann. of Math. (2) 133 (1991), p. 549-576. | DOI | MR | Zbl
- "[36] Transcendence of numbers with a low complexity expansion", J. Number Theory 67 (1997), p. 146-161. | DOI | MR | Zbl
& - "[37] Metamathematical considerations on the relative irreducibility of polynomials", Canad. J. Math. 7 (1955), p. 483-489. | DOI | MR | Zbl
& - "[38] On the number of prime factors of integers of the form ", Acta Arith. 74 (1996), p. 365-385. | DOI | EuDML | MR | Zbl
. & - "[39] On the largest prime factor of ", Bol. Soc. Mat. Mexicana (3) 9 (2003), p. 235-244. | MR | Zbl
& - "[40] Diophantine geometry, an introduction, Graduate Texts in Mathematics, vol. 201, Springer, 2000. | DOI | MR | Zbl
& -[41] Fundamentals of Diophantine geometry, Springer, 1983. | DOI | MR | Zbl
-[42] Équations diophantiennes exponentielles", Invent. Math. 78 (1984), p. 299-327. | DOI | EuDML | MR | Zbl
- "[43] Generalizations of Siegel's and Picard's theorems", arXiv:math.NT/0503699, to appear. | DOI | MR | Zbl
- "[44] Arithmetic properties of the solutions of a class of functional equations", J. reine angew. Math. 330 (1982), p. 159-172. | EuDML | MR | Zbl
& - "[45] Arithmetic properties of automata: regular sequences", J. reine angew. Math. 392 (1988), p. 57-69. | EuDML | MR | Zbl
& , "[46] On the fractional parts of the powers of a rational number. II", Mathematika 4 (1957), p. 122-124. | DOI | MR | Zbl
- "[47] Remarks and problems on finite and periodic continued fractions", Enseign. Math. (2) 39 (1993), p. 249-257. | MR | Zbl
- "[48] An application of W. Schmidt's theorem: transcendental numbers and golden number", Fibonacci Quart. 15 (1977), p. 15-16. | MR | Zbl
- "[49] Holomorphic curves and integral points off divisors", Math. Z. 239 (2002), p. 593-610. | DOI | MR | Zbl
& - "[50] The -adic generalization of the Thue-Siegel-Roth theorem", Mathematika 5 (1958), p. 40-48. | DOI | MR | Zbl
- "[51] Rational approximations to algebraic numbers", Mathematika 2 (1955), p. 1-20; corrigendum, 168. | DOI | MR | Zbl
- "[52] The subspace theorem and applications", in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), vol. Extra Vol. II, Doc. Math., 1998, Extra Vol. II, p. 197-205 (electronic). | EuDML | MR | Zbl
- "[53] Die -adische Verallgemeinerung des Satzes von Thue-Siegel-Roth-Schmidt", J. reine angew. Math. 288 (1976), p. 86-105. | EuDML | MR | Zbl
, "[54] On products of special linear forms with algebraic coefficients", Acta Arith. 31 (1976), p. 389-398. | DOI | EuDML | MR | Zbl
, "[55] The -adic Thue-Siegel-Roth-Schmidt theorem", Arch. Math. (Basel) 29 (1977), p. 267-270. | DOI | MR | Zbl
, "[56] Multiplicities of recurrence sequences", Acta Math. 176 (1996), p. 171-243. | DOI | MR | Zbl
, "[57] Approximation of algebraic numbers", in Diophantine approximation (Cetraro, 2000), Lecture Notes in Math., vol. 1819, Springer, 2003, p. 107-170. | DOI | MR | Zbl
, "[58] Norm form equations", Ann. of Math. (2) 96 (1972), p. 526-551. | DOI | MR | Zbl
- "[59] Diophantine approximation, Lecture Notes in Mathematics, vol. 785, Springer, 1980. | MR | Zbl
,[60] Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, vol. 1467, Springer, 1991. | MR | Zbl
,[61] On the period of the continued fraction for values of the square root of power sums", Acta Arith. 123 (2006), p. 297-312. | DOI | EuDML | MR | Zbl
- "[62] Über einige Anwendungen Diophantischer Approximationen", Abh. Preuss Akad. Wiss. Phys.-Math. Kl. 1 (1929), p. 209-266. | JFM
- "[63] Diophantine equations with prime unknowns (Russian)", Trudy Mat. Inst. Steklov. 158 (1981), p. 180-196; English translation: Proc. Steklov Inst. Math. 1983, 4, p. 197-214. | MR | Zbl
- "[64] Über Annäherungswerte algebraischer Zahlen", J. reine angew. Math. 135 (1909), p. 284-305. | EuDML | JFM | MR
- "[65] Note on the density constant in the distribution of self-numbers. II", Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 2 (1999), p. 397-399. | EuDML | MR | Zbl
& - "[66] Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer, 1987. | MR | Zbl
-[67] A refinement of Schmidt's subspace theorem", Amer. J. Math. 111 (1989), p. 489-518. | DOI | MR | Zbl
, "[68] Integral points on subvarieties of semiabelian varieties. I", Invent. Math. 126 (1996), p. 133-181. | DOI | MR | Zbl
, "[69] Integral points on subvarieties of semiabelian varieties. II", Amer. J. Math. 121 (1999), p. 283-313. | DOI | MR | Zbl
, "[70] Diophantine analysis and words", in Diophantine analysis and related fields 2006 (in honor of Prof. Iekata Shiokawa), Sem. Math. Sci., vol. 35, Keio Univ., 2006, p. 203-221. | MR | Zbl
- "[71] Hilbert irreducibility sequences and nonstandard arithmetic", J. Number Theory 26 (1987), p. 274-285. | DOI | MR | Zbl
- "[72] Note on dense universal Hilbert sets", C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), p. 703-706. | MR | Zbl
- "[73] A proof of Pisot's -th root conjecture", Ann. of Math. (2) 151 (2000), p. 375-383. | DOI | EuDML | MR | Zbl
, "[74] Some applications of diophantine approximation to diophantine equations (with special emphasis on the Schmidt subspace theorem)", Forum, Udine, 2003.
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