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arXiv · 2507.10163

Linear independence of powers for polynomials

Alexandru Crăciun
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Abstract

Given $k \ge 2$ polynomials in $d \ge 1$ variables with coefficients in a field of characteristic $0$, such that no two are linearly dependent, we show that for any integer $r$ greater than $\max\left\{k {k-1 \choose 2}, 2\right\}$, the $r$-th powers of the polynomials are linearly independent.

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Alexandru Crăciun. 2025-07-14. Linear independence of powers for polynomials. https://arxiv.org/abs/2507.10163

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