An inverse theorem for generalized arithmetic progression with mild multiplicative property

TL;DR

This paper establishes a structural theorem for generalized arithmetic progressions in finite fields that contain large product sets, advancing understanding of their multiplicative properties.

Contribution

It introduces a new inverse theorem characterizing generalized arithmetic progressions with mild multiplicative properties in finite fields.

Findings

Structural characterization of progressions with large product sets

Insights into multiplicative behavior of generalized arithmetic progressions

Advancement in additive combinatorics in finite fields

Abstract

We prove a structural theorem for generalized arithmetic progressions in $\F_p$ which contain a large product set of two other progressions.