On the number of solutions of polynomial congruences and Thue equations
Journal of the American Mathematical Society, Tome 04 (1991) no. 4, pp. 793-835

Voir la notice de l'article provenant de la source American Mathematical Society

@article{10_1090_S0894_0347_1991_1119199_X,
     author = {Stewart, C. L.},
     title = {On the number of solutions of polynomial congruences and {Thue} equations},
     journal = {Journal of the American Mathematical Society},
     pages = {793--835},
     publisher = {mathdoc},
     volume = {04},
     number = {4},
     year = {1991},
     doi = {10.1090/S0894-0347-1991-1119199-X},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-1991-1119199-X/}
}
TY  - JOUR
AU  - Stewart, C. L.
TI  - On the number of solutions of polynomial congruences and Thue equations
JO  - Journal of the American Mathematical Society
PY  - 1991
SP  - 793
EP  - 835
VL  - 04
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-1991-1119199-X/
DO  - 10.1090/S0894-0347-1991-1119199-X
ID  - 10_1090_S0894_0347_1991_1119199_X
ER  - 
%0 Journal Article
%A Stewart, C. L.
%T On the number of solutions of polynomial congruences and Thue equations
%J Journal of the American Mathematical Society
%D 1991
%P 793-835
%V 04
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-1991-1119199-X/
%R 10.1090/S0894-0347-1991-1119199-X
%F 10_1090_S0894_0347_1991_1119199_X
Stewart, C. L. On the number of solutions of polynomial congruences and Thue equations. Journal of the American Mathematical Society, Tome 04 (1991) no. 4, pp. 793-835. doi: 10.1090/S0894-0347-1991-1119199-X

[1] Amice, Yvette Les nombres 𝑝-adiques 1975 190

[2] Bombieri, Enrico On the Thue-Siegel-Dyson theorem Acta Math. 1982 255 296

[3] Bombieri, E. On the Thue-Mahler equation 1987 213 243

[4] Bombieri, E., Schmidt, W. M. On Thue’s equation Invent. Math. 1987 69 81

[5] De Bruijn, N. G. On the number of positive integers ≤𝑥 and free of prime factors >𝑦 Nederl. Akad. Wetensch. Proc. Ser. A 1951 50 60

[6] Chalk, J. H. H., Smith, R. A. Sándor’s theorem on polynomial congruences and Hensel’s lemma C. R. Math. Rep. Acad. Sci. Canada 1982 49 54

[7] Erdã¶S, P., Stewart, C. L., Tijdeman, R. Some Diophantine equations with many solutions Compositio Math. 1988 37 56

[8] Evertse, Jan-Hendrik On the equation 𝑎𝑥ⁿ-𝑏𝑦ⁿ Compositio Math. 1982 289 315

[9] Evertse, J.-H. On equations in 𝑆-units and the Thue-Mahler equation Invent. Math. 1984 561 584

[10] Evertse, J.-H., Gyå‘Ry, K. Thue-Mahler equations with a small number of solutions J. Reine Angew. Math. 1989 60 80

[11] Evertse, J.-H., Gyå‘Ry, K. Effective finiteness results for binary forms with given discriminant Compositio Math. 1991 169 204

[12] Evertse, J.-H., Gyå‘Ry, K., Stewart, C. L., Tijdeman, R. On 𝑆-unit equations in two unknowns Invent. Math. 1988 461 477

[13] Hardy, G. H., Wright, E. M. An introduction to the theory of numbers 1979

[14] Huxley, M. N. A note on polynomial congruences 1981 193 196

[15] Lang, Serge Integral points on curves Inst. Hautes Études Sci. Publ. Math. 1960 27 43

[16] Lewis, D. J., Mahler, K. On the representation of integers by binary forms Acta Arith. 1960/61 333 363

[17] Loxton, John H., Smith, Robert A. On Hua’s estimate for exponential sums J. London Math. Soc. (2) 1982 15 20

[18] Mahler, Kurt Zur Approximation algebraischer Zahlen. II Math. Ann. 1933 37 55

[19] Mahler, K. An inequality for the discriminant of a polynomial Michigan Math. J. 1964 257 262

[20] Mordell, L. J. Diophantine equations 1969

[21] Moree, P., Stewart, C. L. Some Ramanujan-Nagell equations with many solutions Indag. Math. (N.S.) 1990 465 472

[22] Mueller, J., Schmidt, W. M. Thue’s equation and a conjecture of Siegel Acta Math. 1988 207 247

[23] Newman, Morris Integral matrices 1972

[24] Sã¡Ndor, Gyula Uber die Anzahl der Lösungen einer Kongruenz Acta Math. 1952 13 16

[25] Schmidt, Wolfgang M. Thue equations with few coefficients Trans. Amer. Math. Soc. 1987 241 255

[26] Siegel, Carl Ludwig Die Gleichung 𝑎𝑥ⁿ–𝑏𝑦ⁿ Math. Ann. 1937 57 68

[27] Silverman, J. H. Representations of integers by binary forms and the rank of the Mordell-Weil group Invent. Math. 1983 281 292

[28] Silverman, Joseph H. Integer points on curves of genus 1 J. London Math. Soc. (2) 1983 1 7

[29] Silverman, Joseph H. The arithmetic of elliptic curves 1986

Cité par Sources :