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- W2952503616 abstract "Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape $0<|F(x, y)| leq h$, where $F(x , y) =(alpha x + beta y)^r -(gamma x + delta y)^r in mathbb{Z}[x ,y]$, $alpha$, $beta$, $gamma$ and $delta$ are algebraic constants with $alphadelta-betagamma neq 0$, and $r geq 3$ and $h$ are integers. As an important application, we pay special attention to the binomial Thue's inequaities $|ax^r - by^r| leq c$. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement by Evertse." @default.
- W2952503616 created "2019-06-27" @default.
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- W2952503616 date "2016-03-10" @default.
- W2952503616 modified "2023-09-27" @default.
- W2952503616 title "Thue's inequalities and the hypergeometric method" @default.
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- W2952503616 hasPublicationYear "2016" @default.
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