@incollection{XUPS_2005____163_0, author = {Guillaume Hanrot}, title = {Quelques id\'ees sur l{\textquoteright}algorithmique des~\'equations diophantiennes}, booktitle = {Th\'eorie algorithmique des nombres et \'equations diophantiennes}, series = {Journ\'ees math\'ematiques X-UPS}, pages = {163--193}, publisher = {Les \'Editions de l{\textquoteright}\'Ecole polytechnique}, year = {2005}, doi = {10.5802/xups.2005-03}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-03/} }
TY - JOUR AU - Guillaume Hanrot TI - Quelques idées sur l’algorithmique des équations diophantiennes JO - Journées mathématiques X-UPS PY - 2005 SP - 163 EP - 193 PB - Les Éditions de l’École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-03/ DO - 10.5802/xups.2005-03 LA - fr ID - XUPS_2005____163_0 ER -
%0 Journal Article %A Guillaume Hanrot %T Quelques idées sur l’algorithmique des équations diophantiennes %J Journées mathématiques X-UPS %D 2005 %P 163-193 %I Les Éditions de l’École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-03/ %R 10.5802/xups.2005-03 %G fr %F XUPS_2005____163_0
Guillaume Hanrot. Quelques idées sur l’algorithmique des équations diophantiennes. Journées mathématiques X-UPS (2005), pp. 163-193. doi : 10.5802/xups.2005-03. https://proceedings.centre-mersenne.org/articles/10.5802/xups.2005-03/
[1] A. Baker Linear forms in the logarithms of algebraic numbers I, Mathematika, Volume 13 (1966), pp. 204-216 II, ibid. 14 (1967), p. 102-107 ; III, ibid. 14 (1967), p. 220-228 ; IV, ibid. 15 (1968), p. 204-216 | DOI | MR | Zbl
[2] A. Baker Contributions to the theory of Diophantine equations. I. On the representation of integers by binary forms, Philos. Trans. Roy. Soc. London Ser. A, Volume 263 (1968), pp. 173-191 II. The Diophantine equation , ibid. 263 (1968), p. 193-208 | DOI | MR | Zbl
[3] A. Baker; H. Davenport The equations and , Quart. J. Math. Oxford Ser. (2), Volume 20 (1969), pp. 129-137 | DOI | MR | Zbl
[4] A. Baker; G. Wüstholz Logarithmic forms and group varieties, J. reine angew. Math., Volume 442 (1993), pp. 19-62 | DOI | MR | Zbl
[5] Karim Belabas L’algorithmique de la théorie algébrique des nombres, Théorie algorithmique des nombres et équations diophantiennes (Journées X-UPS), Les Éditions de l’École polytechnique, Palaiseau, 2005 (Ce volume) | DOI
[6] Yu. Bilu Solving superelliptic Diophantine equations by Baker’s method (1994) (prépublication)
[7] Yu. Bilu; G. Hanrot Solving superelliptic Diophantine equations by Baker’s method, Compositio Math., Volume 112 (1998), pp. 273-312 | DOI | MR | Zbl
[8] Yu. Bilu; G. Hanrot; P. Voutier Existence of primitive divisors of Lucas and Lehmer sequences (with an appendix by M. Mignotte), J. reine angew. Math., Volume 539 (2001), pp. 75-122 | Zbl
[9] F. Dyson The approximation to algebraic numbers by rationals, Acta Math., Volume 79 (1947), pp. 225-240 | DOI | MR | Zbl
[10] A.O. Gelfond Transcendental and algebraic numbers, Dover Publications, NewYork, 1960 (traduction anglaise)
[11] M. Laurent; M. Mignotte; Y. Nesterenko Formes linéaires en deux logarithmes et déterminants d’interpolation, J. Number Theory, Volume 65 (1995), pp. 285-321 | DOI | Zbl
[12] A.K. Lenstra; H.W. Lenstra; L. Lovász Factoring polynomials with rational coefficients, Math. Ann., Volume 261 (1982), pp. 515-534 | DOI | MR | Zbl
[13] Yu. Matijasevič Enumerable sets are diophantine, Soviet Math. Doklady, Volume 11 (1970), pp. 354-358 version anglaise complétée : Soviet Math. Doklady, 12 (1971), p. 249-54 | Zbl
[14] K.F. Roth Rational approximations to algebraic numbers, Mathematika, Volume 2 (1955), pp. 1-20 | DOI | Zbl
[15] C.L. Siegel Approximation algebraischer Zahlen, Math. Z., Volume 10 (1921), pp. 173-213 | DOI | MR | Zbl
[16] N.P. Smart The algorithmic resolution of Diophantine equations : a computational cookbook, London Math. Soc. Student Texts, 41, Cambridge University Press, Cambridge, 1998 | DOI
[17] R. Stroeker; N. Tzanakis Solving elliptic Diophantine equations by estimating linear forms in elliptic logarithms, Acta Arith., Volume 67 (1994), pp. 177-196 | DOI | MR | Zbl
[18] A. Thue Über Annäherungswerte algebraischer Zahlen, J. reine angew. Math., Volume 135 (1909), pp. 284-305 | DOI | MR | Zbl
[19] N. Tzanakis; B.M.M. de Weger On the practical solution of the Thue equation, J. Number Theory, Volume 31 (1989), pp. 99-132 | DOI | MR | Zbl
[20] I. Vardi Archimedes’ Cattle problem, Amer. Math. Monthly, Volume 105 (1998), pp. 305-319 | DOI | MR | Zbl
[21] B.M.M. de Weger Solving exponential diophantine equations using lattice basis reduction algorithms, J. Number Theory, Volume 26 (1987), pp. 325-367 | DOI | MR | Zbl
Cité par Sources :