Diophantine approximation of polynomials over \mathbbF_q[t] satisfying a divisibility condition

2015/09/04 by Shuntaro Yamagishi, Yamagishi, Shuntaro · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Analytic Number Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1509.01560

Abstract

Let \mathbbF_q[t] denote the ring of polynomials over \mathbbF_q, the finite field of q elements. We prove an estimate for fractional parts of polynomials over \mathbbF_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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