Lower bounds for the Wiener norm in $\mathbb{Z}_p^d$

TL;DR

This paper establishes lower bounds for the Wiener norm of functions defined on the finite group , , providing insights into the Fourier analysis of functions on finite abelian groups.

Contribution

It introduces new lower bounds for the Wiener norm in , advancing understanding of Fourier norms in finite group settings.

Findings

Derived explicit lower bounds for the Wiener norm in 

Extended Fourier analysis techniques to higher-dimensional finite groups

Provided theoretical insights into the structure of functions with small Fourier norms

Abstract

We obtain lower bounds for the $l_1$-norm of the Fourier transform of functions on $\mathbb{Z}_p^d$.