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S-unit equation in two variables and Padé approximations.
- Source :
-
International Journal of Number Theory . Bov2023, Vol. 19 Issue 10, p2427-2442. 16p. - Publication Year :
- 2023
-
Abstract
- In this paper, we use Padé approximations, constructed in [Kawashima and Poëls, Padé approximations for shifted functions and parametric geometry of numbers, J. Number Theory 243 (2023) 646–687] for binomial functions, to give a new upper bound for the number of the solutions of the S -unit equation in two variables. Combining explicit Padé approximants with a simple argument relying on Mahler measure as well as the local height, we refine the bound due to Evertse [On equations in S -units and the Thue-Mahler equation, Invent. Math. 75 (1984) 561–584]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NUMBER theory
*EQUATIONS
*HYPERGEOMETRIC functions
Subjects
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 19
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 173821694
- Full Text :
- https://doi.org/10.1142/S1793042123501191