Convolution and square in abelian groups III
Number Theory
2024-01-09 v1
Abstract
In the first paper we proved that on the cyclic groups of odd order d, there exist non zero functions whose convolution square f*f(2t) is proportional to their square f(t)^2 when the proportionality constant is an odd algebraic integer of norm d whose both real and imaginary part are square roots of integers. We show here that the function f can be chosen to be equal to the conjugate of its Fourier transform.
Cite
@article{arxiv.2401.03716,
title = {Convolution and square in abelian groups III},
author = {Yves Benoist},
journal= {arXiv preprint arXiv:2401.03716},
year = {2024}
}