Convolution and square in abelian groups III

2024/01/08 by Benoist, Yves
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.03716

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.

Related

• Convolution and square in abelian groups I
• Convolution and square in abelian groups II
• Integral transforms characterized by convolution
• Higher order Fourier analysis as an algebraic theory III
• Invertibility of convolution operators on homogeneous groups