Paucity phenomena for polynomial products

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-31 DOI:10.1112/blms.13095

Victor Y. Wang, Max Wenqiang Xu

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Abstract

Let $P (x) \in Z [x]$ be a polynomial with at least two distinct complex roots. We prove that the number of solutions $(x_{1}, \dots, x_{k}, y_{1}, \dots, y_{k}) \in {[N]}^{2 k}$ to the equation

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多项式积的贫乏现象

让 P ( x ) ∈ Z [ x ] $P(x)\in \mathbb {Z}[x]$ 是一个至少有两个不同复根的多项式。我们证明解的个数 ( x 1 , ⋯ , x k , y 1 , ⋯ , y k ) ∈[N]2k$(x_1, \dots, x_k, y_1, \dots, y_k)\in [N]^{2k}$ 解方程

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