Romanoff's theorem for polynomials over finite fields revisited
Yuchen Ding, Haiyan Zhou · Acta Arithmetica · 2021
Let $g$ be a given polynomial of positive degree over a finite field. Shparlinski and Weingartner proved that the proportion of monic polynomials of degree $n$ which can be represented as $h+g^k$ has the order of magnitude $1/\mathrm {deg} g$, where