Waring's problem for polynomial biquadrates over a finite field of odd characteristic

Abstract

Let $q$ be a power of an odd prime $p$ and let ${k}$ be a finite field with $q$ elements. Our main result is: If $q \notin \{3,9,5,13,17,25,29\},$ every polynomial $P\in{k}[t]$ of degree $\geq 269$ is a strict sum of 11 biquadrates. We first decompose $P$ as a strict mixed sum of biquadrates.