On the Odlyzko-Stanley enumeration problem and Waring's problem over finite fields

Jiyou Li

We obtain an asymptotic formula on the Odlyzko-Stanley enumeration problem. Let $N_m^{\ast }(k,b)$ be the number of $k$-subsets $S\subseteq F_p^{\ast }$ such that ${\sum }_{x\in S}{x}^m=b$. If $m<p…