On the Lower Bound of the Divisibility of Exponential Sums in Binomial Case

TL;DR

This paper investigates the lower bounds of divisibility for exponential sums related to binomials over finite fields, building on prior exact calculations and conjectures in the area.

Contribution

It provides new insights into the divisibility properties of exponential sums for binomials, extending previous exact results and proposing related conjectures.

Findings

Established lower bounds for divisibility of exponential sums

Extended understanding of binomial exponential sums over finite fields

Proposed conjectures for future research

Abstract

Francis Castro, et al [2] computed the exact divisibility of families of exponential sums associated to binomials $F(X) = aX^{d_1} + bX^{d_2}$ over $\mathbb{F}_p$, and a conjecture is presented for related work. Here we study this question.