Diophantine approximation of polynomials over $\mathbb{F}_q[t]$ satisfying a divisibility condition

Shuntaro Yamagishi

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arXiv · 1509.01560

Diophantine approximation of polynomials over $\mathbb{F}_q[t]$ satisfying a divisibility condition

Shuntaro Yamagishi

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Abstract

Let $\mathbb{F}_q[t]$ denote the ring of polynomials over $\mathbb{F}_q$, the finite field of $q$ elements. We prove an estimate for fractional parts of polynomials over $\mathbb{F}_q[t]$ satisfying a certain divisibility condition analogous to that of intersective polynomials in the case of integers. We then extend our result to consider linear combinations of such polynomials as well.

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Shuntaro Yamagishi. 2015-09-04. Diophantine approximation of polynomials over $\mathbb{F}_q[t]$ satisfying a divisibility condition. https://arxiv.org/abs/1509.01560

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