Convolution and square in abelian groups III

Yves Benoist

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arXiv · 2401.03716

Convolution and square in abelian groups III

Yves Benoist

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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.

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Yves Benoist. 2024-01-08. Convolution and square in abelian groups III. https://arxiv.org/abs/2401.03716

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