An Asymptotic Formula For Counting Subset Sums Over Subgroups Of Finite Fields

TL;DR

This paper derives a precise asymptotic estimate for counting k-element subsets within a subgroup of a finite field that sum to a specific element, advancing understanding of subset sum distributions in finite fields.

Contribution

It provides a sharp asymptotic formula for the number of k-element subsets of a subgroup summing to a given element in finite fields, a novel result in finite field combinatorics.

Findings

Established a sharp estimate for subset sums over subgroups

Extended understanding of subset sum distributions in finite fields

Provided tools for further combinatorial and algebraic investigations

Abstract

Let F_q be the finite field of q elements. Let H be a multiplicative subgroup of F_q^*. For a positive integer k and element b\in F_q, we give a sharp estimate for the number of k-element subsets of H which sum to b.