An explicit polynomial analogue of Romanoff's theorem

2015/10/30 by Igor E. Shparlinski, Shparlinski, Igor E., Andreas J. Weingartner +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1510.08991

arxiv created 2015/10/30 · arxiv updated 2015/11/02

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/°g.

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