The Number of Solutions of Polynomial-Exponential Equations

Compositio Mathematica

Volumn 120, Issue 2, 2000, Pages 193-225

  Schlickewei, H P ^a   Schmidt, W M ^b  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Exponential diophantine equations; Linear recurrence sequences

Indexed keywords

EID: 0010661598     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1001719425893     Document Type: Article

References (19)

1. Bombieri, E. and Mueller, J.: On a conjecture of Siegel, Monatsh. Math. 125 (1998), 293-308.
2. Cassels, J. W. S.: An Introduction to the Geometry of Numbers, Grundlehren Math. Wiss. 99, Springer, New York, 1959.
3. Dobrowolski, E.: On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401.
4. Evertse, J. H.: An improvement of the quantitative subspace theorem, Compositio Math. 101 (1996), 225-311.
5. Evertse, J.H., Györy, K., Stewart, C. L. and Tijdeman. R.: On S-unit equations in two unknowns, Invent. Math. 92 (1988), 461-477.
6. Evertse, J. H. and Schlickewei, H. P.: A quantitative version of the absolute subspace theorem, (to appear).
7. Evertse, J. H., Schlickewei, H. P. and Schmidt, W. M.: Linear equations in variables which Lie in a multiplicative group, (to appear).
8. Faltings, G.: Diophantine approximation on abelian varieties, Ann. of Math. 113 (1991), 549-576.
9. Laurent, M.: Équations exponentielles-polynômes et suites récurrentes linéaires, Astérisque 147-148 (1987), 121-139.
10. Laurent, M.: Équations exponentielles-polynômes et suites récurrentes linéaires, II, J. Number Theory 31 (1989), 24-53.
11. Rogers, C. A.: A note on coverings and packings, J. London Math. Soc. 25 (1950), 327-331.
12. Rogers, C. A.: A note on coverings, Mathematika 4 (1957), 1-6.
13. Schlickewei, H. P.: S-unit equations over number fields, Invent. Math. 102 (1990), 95-107.
14. Schlickewei, H. P.: Multiplicities of recurrence sequences, Acta Math. 176 (1996), 171-243.
15. Schlickewei, H. P.: Lower bounds for heights on finitely generated groups, Monatsh. Math. 123 (1997), 171-178.
16. Schlickewei, H. P. and Schmidt, W. M.: On polynomial exponential equations, Math. Ann. 296 (1993), 339-361.
17. Schlickewei, H. P. and Schmidt, W. M.: Linear equations in members of recurrence sequences, Ann. Scuola Norm. Sup. Pisa, Serie Fis. e Mat. 20 (1993), 219-246.
18. Schlickewei, H. P. and Schmidt, W. M.: The intersection of recurrence sequences, Acta Arith. 72 (1995), 1-44.
19. Schmidt, W. M.: Heights of algebraic points lying on curves or hypersurfaces, Proc. Amer. Math. Soc. 124 (1996), 3003-3013.