On Wiener norm of subsets of Z_p of medium size

TL;DR

This paper establishes a lower bound for the Wiener norm of characteristic functions of subsets in Z_p when the subset size is medium, specifically between exponential and a third of p.

Contribution

It provides a new lower bound for Wiener norms of subsets of Z_p in the medium size range, advancing understanding of harmonic analysis on finite groups.

Findings

Lower bound for Wiener norm when |A| is between exponential and p/3

Applicable to prime modulus p

Enhances previous bounds in harmonic analysis

Abstract

We give a lower bound for Wiener norm of characteristic function of subsets A from Z_p, p is a prime number, in the situation when exp((log p/log log p)^{1/3}) \le |A| \le p/3.