Convolution and Square in Abelian Groups I

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2022-05-18 DOI:10.1080/10586458.2023.2174212

Y. Benoist

引用次数: 2

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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阿贝尔群I中的卷积和平方

证明了在奇阶d的循环群上存在非零函数，其卷积的平方f*f(2t)与它们的平方f(t)^2成正比，且比例常数由范数d的虚二次整数取1模2给出。这个证明涉及到椭圆曲线上的函数和复数乘法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.