Convolution and square in abelian groups I
Number Theory
2022-08-04 v2
Abstract
We prove 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 given by an imaginary quadratic integer of norm d which is equal to 1 modulo 2. The proof involves theta functions on elliptic curves with complex multiplication.
Cite
@article{arxiv.2205.08749,
title = {Convolution and square in abelian groups I},
author = {Yves Benoist},
journal= {arXiv preprint arXiv:2205.08749},
year = {2022}
}