@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},
year = {2008},
publisher = {Soci\'et\'e math\'ematique de France},
number = {317},
mrnumber = {2487729},
zbl = {1220.11091},
language = {en},
url = {https://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 - https://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 https://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.. https://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. | MR | Zbl | DOI
[2] & , "On the complexity of algebraic numbers. I. Expansions in integer bases", Ann. of Math. (2) 165 (2007), p. 547-565. | MR | Zbl | DOI
[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. | MR | Zbl | DOI
[5] & - Automatic sequences. Theory, applications, generalizations, Cambridge University Press, 2003. | MR | Zbl
[6] & (eds.) - 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
[7] - "Géométrie des surfaces algébriques et points entiers", arXiv:math.NT/0606184. | MR | Numdam
[8] - "A note on universal Hilbert sets", J. reine angew. Math. 479 (1996), p. 195-203. | MR | Zbl | EuDML
[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. | JFM | DOI
[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. | MR | Zbl | DOI
[13] & - "A quantitative lower bound for the greatest prime factor of ", Acta Arith. 114 (2004), p. 275-294. | MR | Zbl | DOI
[14] , "On the period of the continued fraction expansion of ", Indag. Math. N.S. 16 (2005), p. 21-35. | MR | Zbl | DOI
[15] & - "Zur Transzendenz gewisser Reihen", Monatsh. Math. 104 (1987), p. 199-223. | MR | Zbl | EuDML | DOI
[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. | MR | Zbl | DOI
[18] , & - "A lower bound for periods of matrices", Comm. Math. Phys. 252 (2004), p. 535-541. | MR | Zbl | DOI
[19] & - "Diophantine equations with power sums and universal Hilbert sets", Indag. Math. (N.S.) 9 (1998), p. 317-332. | MR | Zbl | DOI
[20] & , "Finiteness of integral values for the ratio of two linear recurrences", Invent. Math. 149 (2002), p. 431-451. | MR | Zbl | DOI
[21] & , "Some new applications of the subspace theorem", Compositio Math. 131 (2002), p. 319-340. | MR | Zbl | DOI
[22] & , "A subspace theorem approach to integral points on curves", C. R. Math. Acad. Sci. Paris 334 (2002), p. 267-271. | MR | Zbl | DOI
[23] & , "On the greatest prime factor of ", Proc. Amer. Math. Soc. 131 (2003), p. 1705-1709. | MR | Zbl | DOI
[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. | MR | Zbl | DOI
[26] & , "On integral points on surfaces", Ann. of Math. (2) 160 (2004), p. 705-726. | MR | Zbl | DOI
[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. | MR | Zbl | DOI
[28] & , "A lower bound for the height of a rational function at S-unit points", Monatsh. Math. 144 (2005), p. 203-224. | MR | Zbl | DOI
[29] & , "On the length of the continued fraction for values of quotients of power sums", J. Théor. Nombres Bordeaux 17 (2005), p. 737-748. | MR | Zbl | EuDML | Numdam | DOI
[30] & , "-unit points on analytic hypersurfaces", Ann. Sci. École Norm. Sup. (4) 38 (2005), p. 76-92. | MR | Zbl | EuDML | DOI | Numdam
[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. | MR | Zbl | DOI
[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. | MR | Zbl | DOI
[36] & - "Transcendence of numbers with a low complexity expansion", J. Number Theory 67 (1997), p. 146-161. | MR | Zbl | DOI
[37] & - "Metamathematical considerations on the relative irreducibility of polynomials", Canad. J. Math. 7 (1955), p. 483-489. | MR | Zbl | DOI
[38] . & - "On the number of prime factors of integers of the form ", Acta Arith. 74 (1996), p. 365-385. | MR | Zbl | EuDML | DOI
[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. | MR | Zbl | DOI
[41] - Fundamentals of Diophantine geometry, Springer, 1983. | MR | Zbl | DOI
[42] - "Équations diophantiennes exponentielles", Invent. Math. 78 (1984), p. 299-327. | MR | Zbl | EuDML | DOI
[43] - "Generalizations of Siegel's and Picard's theorems", arXiv:math.NT/0503699, to appear. | Zbl | MR | DOI
[44] & - "Arithmetic properties of the solutions of a class of functional equations", J. reine angew. Math. 330 (1982), p. 159-172. | MR | Zbl | EuDML
[45] & , "Arithmetic properties of automata: regular sequences", J. reine angew. Math. 392 (1988), p. 57-69. | MR | Zbl | EuDML
[46] - "On the fractional parts of the powers of a rational number. II", Mathematika 4 (1957), p. 122-124. | MR | Zbl | DOI
[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. | MR | Zbl | DOI
[50] - "The -adic generalization of the Thue-Siegel-Roth theorem", Mathematika 5 (1958), p. 40-48. | MR | Zbl | DOI
[51] - "Rational approximations to algebraic numbers", Mathematika 2 (1955), p. 1-20; corrigendum, 168. | MR | Zbl | DOI
[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). | MR | Zbl | EuDML
[53] , "Die -adische Verallgemeinerung des Satzes von Thue-Siegel-Roth-Schmidt", J. reine angew. Math. 288 (1976), p. 86-105. | MR | Zbl | EuDML
[54] , "On products of special linear forms with algebraic coefficients", Acta Arith. 31 (1976), p. 389-398. | MR | Zbl | EuDML | DOI
[55] , "The -adic Thue-Siegel-Roth-Schmidt theorem", Arch. Math. (Basel) 29 (1977), p. 267-270. | MR | Zbl | DOI
[56] , "Multiplicities of recurrence sequences", Acta Math. 176 (1996), p. 171-243. | MR | Zbl | DOI
[57] , "Approximation of algebraic numbers", in Diophantine approximation (Cetraro, 2000), Lecture Notes in Math., vol. 1819, Springer, 2003, p. 107-170. | MR | Zbl | DOI
[58] - "Norm form equations", Ann. of Math. (2) 96 (1972), p. 526-551. | MR | Zbl | DOI
[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. | MR | Zbl | EuDML | DOI
[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. | MR | JFM | EuDML
[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. | MR | Zbl | EuDML
[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. | MR | Zbl | DOI
[68] , "Integral points on subvarieties of semiabelian varieties. I", Invent. Math. 126 (1996), p. 133-181. | MR | Zbl | DOI
[69] , "Integral points on subvarieties of semiabelian varieties. II", Amer. J. Math. 121 (1999), p. 283-313. | MR | Zbl | DOI
[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. | MR | Zbl | DOI
[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. | MR | Zbl | EuDML | DOI
[74] , "Some applications of diophantine approximation to diophantine equations (with special emphasis on the Schmidt subspace theorem)", Forum, Udine, 2003.







