Upper bounds for the numbers of solutions of unit equations in two unknowns (Q1324837)
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scientific article; zbMATH DE number 578631
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Upper bounds for the numbers of solutions of unit equations in two unknowns |
scientific article; zbMATH DE number 578631 |
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Upper bounds for the numbers of solutions of unit equations in two unknowns (English)
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19 July 1994
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The author considers the equation \(ax + by = 1\), in which the coefficients \(a, b \in \mathbb{C}^*\) and the unknowns \(x\), \(y\) belong to a subgroup \(\Gamma\) of \(\mathbb{C}^*\) of finite rank and computes an explicit upper bound for the number of its solutions. This extends to the most general case an earlier result by \textit{J. H. Evertse} and the author [J. Reine Angew. Math. 358, 6-19 (1985; Zbl 0552.10010)].
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numbers of solutions
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unit equation
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subgroup of finite rank
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explicit upper bound
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