On the Odlyzko–Stanley enumeration problem and Waringʼs problem over finite fields

Abstract

We obtain an asymptotic formula on the Odlyzko-Stanley enu-In addition, let γ ′ (m, p) denote the distinct Waring's number (mod p), the smallest positive integer k such that every integer is a sum of m-th powers of k-distinct elements (mod p). The above bound implies that there is a constant ǫ(δ) > 0 such for any prime p and any m < p 1−δ , if ǫ −1 < (e − 1)p δ−ǫ , then γ ′ (m, p) ≤ ǫ −1 .

Counting polynomial subset sums

“…By combining Bourgain's bound and Li and Wan's sieving technique [20], Li [18] proved a refined result that if d < p 1−δ , then there is a constant 0 < ǫ = ǫ(δ) < δ such that…”

Applications Of The Subset Sum Problem Over Finite Abelian Groups

“…Odlyzko and Stanley [12] used Dirichlet characters to estimate S Fp (F * p ) r,x N , b . Li [7] improved the estimate using the sieve formula. When q is a power of p, Zhu and Wan [18] estimated the number of solutions to the diagonal equation…”