论文标题
可对角线的thue方程 - 重新审视
Diagonalizable Thue Equations -- revisited
论文作者
论文摘要
让$ r，h \ in \ mathbb {n} $带$ r \ geq 7 $，让$ f（x，y）\ in \ mathbb {z} [x，y] $是二进制形式，使得 \ [ f（x，y）=（αx +βy）^r-（γx +Δy）^r， \]其中$α$，$β$，$γ$和$δ$是代数常数，$αδ-βγ\ neq 0 $。我们为THUE不等式的原始解决方案数量建立上限$ 0 <| F（x，y）| \ leq H $，改善了Siegel和Akhtari，Saradha＆Sharma的早期结果。
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 \[ F(x , y) =(αx + βy)^r -(γx + δy)^r, \] where $α$, $β$, $γ$ and $δ$ are algebraic constants with $αδ-βγ\neq 0$. 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.
