In this paper, we will study the connections between the mirror symmetry of Calabi-Yau threefolds and Deligne's conjecture on the special values of the L-functions of critical motives. Using the theory of mirror symmetry, we will develop a method to compute the Deligne's period for a Calabi-Yau threefold in the mirror family of a one-parameter mirror pair. We will give two examples to show how this method works, and we will express the Deligne's period in terms of the classical periods of the threeform. Using this method, we will compute the Deligne's period of a Calabi-Yau threefold studied in a recent paper by Candelas, de la Ossa, Elmi and van Straten. Based on their numerical results, we will explicitly show that this Calabi-Yau threefold satisfies Deligne's conjecture. A second purpose of this paper is to introduce the Deligne's conjecture to the physics community, and provide further evidence that there might exist interesting connections between physics and number theory.

在本文中，我们将研究Calabi-Yau三重镜的对称性与关于L的特殊值的Deligne猜想之间的联系关键动机的功能。使用镜像对称性理论，我们将开发一种方法来计算单参数镜像对的镜像族中Calabi-Yau三倍的Deligne周期。我们将给出两个示例来说明此方法的工作原理，并以三种形式的经典周期来表示Deligne的周期。使用这种方法，我们将计算Candelas，de la Ossa，Elmi和van Straten在最近的论文中研究的Calabi-Yau三倍的Deligne周期。根据他们的数值结果，我们将明确表明，Calabi-Yau三倍满足Deligne的猜想。本文的第二个目的是向物理学界介绍德利涅的猜想，并提供进一步的证据表明物理学与数论之间可能存在有趣的联系。