Fourier transform in cyclic groups
Number Theory
2024-07-09 v2
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.
Cite
@article{arxiv.2406.11529,
title = {Fourier transform in cyclic groups},
author = {Yves Benoist},
journal= {arXiv preprint arXiv:2406.11529},
year = {2024}
}
Comments
This version 2 contains a new chapter "Unimodular C-functions for safe prime" that deal with H. Cohn's question for safe primes