Convolution and square in abelian groups III

Yves Benoist (1, 2)

1 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
2 Université Paris-Saclay

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.

Mots clés: Finite Fourier transform; Cyclic group; Elliptic curve; Complex multiplication; Theta function; Jacobi sums; Weil numbers

Domaines: Théorie des nombres [math.NT]

Yves Benoist. Convolution and square in abelian groups III. 2024. ⟨hal-04376989⟩