Fourier transform in cyclic groups

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.

This version 2 contains a new chapter "Unimodular C-functions for safe prime" that deal with H. Cohn's question for safe primes