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arXiv · 1510.08991

An explicit polynomial analogue of Romanoff's theorem

Igor E. Shparlinski·Andreas J. Weingartner
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Abstract

Given a polynomial $g$ of positive degree over a finite field, we show that the proportion of polynomials of degree $n$, which can be written as $h+g^k$, where $h$ is an irreducible polynomial of degree $n$ and $k$ is a nonnegative integer, has order of magnitude $1/\deg g$.

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Igor E. Shparlinski, Andreas J. Weingartner. 2015-10-30. An explicit polynomial analogue of Romanoff's theorem. https://arxiv.org/abs/1510.08991

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