Conjectures for Moments Associated With Cubic Twists of Elliptic Curves

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2021-07-01 DOI:10.1080/10586458.2021.1926002

Chantal David, M. Lalín, J. Nam

引用次数: 1

Abstract

Abstract We extend the heuristic introduced by Conrey, Farmer, Keating, Rubinstein, and Snaith in order to formulate conjectures for the -moments of L-functions of elliptic curves twisted by cubic characters. We also apply the work of Keating and Snaith on the -moments of characteristic polynomials of unitary matrices to extend our conjecture to such that and . Our conjectures are then numerically tested for two families. A novelty of our conjectures is that cubic twists naturally lead us to consider the possibility .

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椭圆曲线三次扭转矩的猜想

摘要我们推广了Conrey、Farmer、Keating、Rubinstein和Snaith提出的启发式方法，以建立对被三次特征扭曲的椭圆曲线的L-函数的-矩的猜想。我们还应用Keating和Snaith关于酉矩阵特征多项式-矩的工作，将我们的猜想推广到这样和。然后，我们对两个族的猜想进行了数值检验。我们猜想的一个新颖之处在于，三次扭曲自然会让我们考虑这种可能性。

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.