An improved sum-product inequality in fields of prime order

TL;DR

This paper enhances the sum-product inequality in prime fields by increasing the exponent from 1/12 to 1/11 for small sets, with a minor logarithmic adjustment.

Contribution

It advances the known bounds of the sum-product inequality in prime fields, improving the exponent in the inequality.

Findings

Exponent improved from 1/12 to 1/11

Applicable to small sets in prime fields

Logarithmic factor included in the result

Abstract

This note improves the best known exponent 1/12 in the prime field sum-product inequality (for small sets) to 1/11, modulo a logarithmic factor.