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arXiv · 2204.12082

Diagonalizable Thue Equations -- revisited

N. Saradha·Divyum Sharma
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Abstract

Let $r,h\in\mathbb{N}$ with $r\geq 7$ and let $F(x,y)\in \mathbb{Z}[x ,y]$ be a binary form such that \[ F(x , y) =(\alpha x + \beta y)^r -(\gamma x + \delta y)^r, \] where $\alpha$, $\beta$, $\gamma$ and $\delta$ are algebraic constants with $\alpha\delta-\beta\gamma \neq 0$. We establish upper bounds for the number of primitive solutions to the Thue inequality $0<|F(x, y)| \leq h$, improving an earlier result of Siegel and of Akhtari, Saradha & Sharma.

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N. Saradha, Divyum Sharma. 2022-04-26. Diagonalizable Thue Equations -- revisited. https://arxiv.org/abs/2204.12082

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