On the distribution of sparse sequences in prime fields and applications

TL;DR

This paper studies how sparse sequences distribute in prime fields and explores their applications in additive number theory and harmonic analysis, providing new distribution results and bounds.

Contribution

It introduces novel distributional results for a broad class of sparse sequences in prime fields with applications to additive problems and the discrete Littlewood problem.

Findings

Distributional properties established for sparse sequences in prime fields

Applications to additive number theory problems

Lower bounds for L1-norms of trigonometric sums

Abstract

In the present paper we investigate distributional properties of sparse sequences modulo almost all prime numbers. We obtain new results for a wide class of sparse sequences which in particular find applications on additive problems and the discrete Littlewood problem related to lower bound estimates of the $L_1$-norm of trigonometric sums.