English

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.

Keywords

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

R2 v1 2026-06-28T17:08:38.205Z