On exponential sums over orbits in ${\mathbb{F}}_p^d$

Abstract

This paper proves a bound for exponential sums over orbits of vectors in ${\mathbb{F}}_p^d$ under subgroups of ${\mathrm{GL}}_{\mathrm{d}}({\mathbb{F}}_{\mathrm{p}})$. The main tool is a classification theorem for approximate groups due to Gill, Helfgott, Pyber, and Szabó.

14 pages; v2: fixed typos, made small exposition changes

References in corpus (2)

• Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak
• Growth in solvable subgroups of GL_r(Z/pZ)