Some recent applications of S-unit equations
Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), p. 17-38
@incollection{AST_1992__209__17_0,
     author = {Gy\"ory, K\'alm\'an},
     title = {Some recent applications of $S$-unit equations},
     booktitle = {Journ\'ees arithm\'etiques de Gen\`eve - 9-13 septembre 1991},
     editor = {Coray D. F. and P\'etermann Y.-F. S},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {209},
     year = {1992},
     pages = {17-38},
     zbl = {0792.11005},
     mrnumber = {1211001},
     language = {en},
     url = {http://www.numdam.org/item/AST_1992__209__17_0}
}
Györy, Kálmán. Some recent applications of $S$-unit equations, in Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), pp. 17-38. http://www.numdam.org/item/AST_1992__209__17_0/

[1] A. Baker, Transcendental Number Theory, 3rd ed., Cambridge University Press, 1990. | MR 1074572 | Zbl 0715.11032

[2] B. J. Birch and J. R. Merriman, Finiteness theorems for binary forms with given discriminant, Proc.London Math.Soc. 25(1972), 385-394. | Article | MR 306119 | Zbl 0248.12002

[3] J. H. Evertse, On sums of S-units and linear recurrences, Compositio Math. 53(1984), 225-244. | Numdam | MR 766298 | Zbl 0547.10008

[4] J. H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent.Math. 75(1984), 561-584. | Article | MR 735341 | Zbl 0521.10015

[5] J. H. Evertse, Decomposable form equations with a small linear scattering, to appear. | MR 1184765 | Zbl 0754.11009

[6] J. H. Evertse and K. Győry, Finiteness criteria for decomposable form equations, Acta Arith. 50(1988), 357-379. | Article | MR 961695 | Zbl 0595.10013

[7] J. H. Evertse and K. Győry, On the numbers of solutions of weighted unit equations, Compositio Math. 66(1988), 329-354. | Numdam | MR 948309 | Zbl 0644.10015

[8] J. H. Evertse and K. Győry, Effective finiteness results for binary forms with given discriminant, Compositio Math. 79(1991), 169-204. | Numdam | MR 1117339 | Zbl 0746.11020

[9] J. H. Evertse and K. Győry, Effective finiteness theorems for decomposable forms of given discriminant, Acta Arith., to appear. | MR 1149860 | Zbl 0746.11019

[10] J. H. Evertse and K. Győry, Discriminants of decomposable forms, to appear. | MR 1198488 | Zbl 0767.11017

[11] J. H. Evertse and K. Győry, C. L. Stewart and R. Tijdeman, S-unit equations and their applications, New Advances in Transcendence Theory (A. Baker ed.), pp.110-174. Cambridge University Press, 1988. | Article | MR 971998 | Zbl 0658.10023

[12] J. H. Evertse and K. Győry, C. L. Stewart and R. Tijdeman, On S-unit equations in two unknowns, Invent.Math. 92(1988), 461-477. | Article | MR 939471 | Zbl 0662.10012

[13] I. M. Gelfand, A. V. Zelevinsky and M. M. Karpanov, On discriminants of polynomials of several variables (Russian), Functional Anal.and Appl. 24(1990), 1-4. | Article | MR 1052262 | Zbl 0719.15003

[14] K. Győry, On the irreducibility of a class of polynomials I, Publ.Math.Debrecen 18(1971), 289-307; | Zbl 0251.12104

K. Győry, On the irreducibility of a class of polynomials II, Publ.Math.Debrecen 19(1972), 293-326 | Zbl 0271.12102

K. Győry, On the irreducibility of a class of polynomials III, J.Number Theory 15 (1982), 164-181 to appear. | Article | MR 675182 | Zbl 0509.12001

[15] K. Győry, On polynomials with integer coefficients and given discriminant I, Acta Arith. 23 (1973), 419-426 | MR 437489 | Zbl 0269.12001

K. Győry, On polynomials with integer coefficients and given discriminant II, Publ.Math.Debrecen 21 (1974), 125-144 | Zbl 0303.12001

K. Győry, On polynomials with integer coefficients and given discriminant III, Publ.Math.Debrecen 23(1976), 141-165 | Zbl 0354.10041

K. Győry, On polynomials with integer coefficients and given discriminant IV, Publ.Math.Debrecen 25(1978), 155-167 | MR 485774 | Zbl 0405.12003

K. Győry, On polynomials with integer coefficients and given discriminant V, Acta Math. Hungar. 32 (1978), 175-190. | MR 498497 | Zbl 0402.10053

[16] K. Győry, On the number of solutions of linear equations in units of an algebraic number field, Comment.Math.Helv. 54 (1979), 583-600. | Article | MR 552678 | Zbl 0437.12004

[17] K. Győry, On certain graphs composed of algebraic integers of a number field and their applications I, Publ.Math.Debrecen 27(1980), 229-242. | MR 603996 | Zbl 0466.05047

[18] K. Győry, On arithmetic graphs associated with integral domains I, in " A Tribute to Paul Erdös" (A. Baker, B. Bollobas, A. Hajnal eds.), Cambridge University Press, 1990, pp.207-222. | Article | MR 1117015 | Zbl 0727.11039

K. Győry, On arithmetic graphs associated with integral domains II in "Sets, Graphs and Numbers", Coll.Math.Soc. J.Bolyai 59, North-Holland Publ.Comp., to appear. | MR 1218202 | Zbl 0798.11042

[19] K. Győry, Upper bounds for the numbers of solutions of unit equations in two unknowns, to appear. | MR 1206381 | Zbl 0814.11018

[20] K. Győry, On the numbers of families of solutions of decomposable form equation systems, to appear. | MR 1208854 | Zbl 0886.11015 | Zbl 0792.11004

[21] K. Győry and A. Schinzel, On a conjecture of Posner and Rumsey, in preparation. | Zbl 0813.11061

[22] L. Hajdú, Some applications of the effective Dirichlet unit theorem, Publ. Math. Debrecen, to appear.

[23] Ch. Hermite, Sur l'introduction des variables continues dans la théorie des nombres, J. reine Angew. Math. 41 (1851), 191-216. | Article | MR 1578717 | Zbl 041.1126cj

[24] J. L. Lagrange, Recherches d'arithmétique, Nouv.Mém.Acad.Berlin, 1773, pp.265-312.

J. L. Lagrange, Recherches d'arithmétique, Oeuvres, III, pp.693-758.

[25] M. Laurent, Equations diophantiennes exponentielles, Invent. Math. 78 (1984), 299-327. | Article | MR 767195 | Zbl 0554.10009

[26] A. J. Van Der Poorten and H. P. Schlickewei, The growth conditions for recurrence sequences, Report 82.0041, Macquarie University, N.S.W.Australia, 1982.

[27] A. J. Van Der Poorten and H. P. Schlickewei, Additive relations in fields, J.Austral.Math.Soc.(Series A) 51(1991), 154-170. | Article | MR 1119694 | Zbl 0747.11017

[28] E. C. Posner and H. Rumsey, Jr., Polynomials that divide infinitely many trinomials, Michigan Math.J. 12(1965), 339-348. | Article | MR 182622 | Zbl 0144.03504

[29] H. P. Schlickewei, The p-adic Thue-Siegel-Roth-Schmidt Theorem, Archiv Math. 29 (1977), 267-270. | Article | MR 491529 | Zbl 0365.10026

[30] H. P. Schlickewei, On norm form equations, J.Number Theory 9 (1977), 370-380. | Article | MR 444562 | Zbl 0365.10016

[31] H. P. Schlickewei, S-unit equations over number fields, Invent. Math. 102 (1990), 95-107. | Article | MR 1069241 | Zbl 0711.11017

[32] H. P. Schlickewei, The quantitative subspace theorem for number fields, to appear. | Numdam | MR 1163217 | Zbl 0751.11033

[33] W. M. Schmidt, Linearformen mit algebraischen Koeffizienten II, Math. Ann. 191(1971), 1-20. | Article | MR 308062 | Zbl 0198.07103

[34] W. M. Schmidt, Norm form equations, Annals of Math. 96(1972), 526-551. | Article | MR 314761 | Zbl 0226.10024

[35] W. M. Schmidt, The subspace theorem in diophantine approximations, Compositio Math. 69(1989), 121-173. | Numdam | MR 984633 | Zbl 0683.10027

[36] W. M. Schmidt, The number of solutions of norm form equations, Trans. Amer. Math. Soc. 317(1990), 197-227. | Article | MR 961596 | Zbl 0693.10014

[37] T. N. Shorey and R. Tljdeman, Exponential diophantine equations, Cambridge University Press, 1986. | MR 891406 | Zbl 1156.11015 | Zbl 0606.10011