Fourier transform in cyclic groups

TL;DR

This paper explores Fourier transforms on cyclic groups, constructing new functions with specific properties and applying Floer homology to problems involving Dirichlet characters and biunimodular functions.

Contribution

It introduces novel functions with constant modulus properties and employs Floer homology to address questions in harmonic analysis on cyclic groups.

Findings

Constructed new functions with Dirichlet character properties

Applied Floer homology to harmonic analysis problems

Provided insights into biunimodular functions

Abstract

On a cyclic group of prime order, the non-trivial Dirichlet characters together with their Fourier transforms have constant modulus outside 0 and vanish at 0. Answering a question of H. Cohn, we construct new functions with these properties. The proof relies on Floer homology. We also apply this method to the biunimodular functions problem.