Convolution and square in abelian groups I

2022/05/18 by Yves Benoist, Benoist, Yves
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2205.08749

openalex publication_date 2022/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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