Mahler/Zeta Correspondence
Mahler/Zeta Correspondence
复制标题
马勒/泽塔通讯
DOI：
10.1007/s11128-022-03644-0
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发表时间：
2022
影响因子：
2.5
通讯作者：
Tamura Shunya
中科院分区：
文献类型：
--
作者：
Komatsu Takashi;Konno Norio;Sato Iwao;Tamura Shunya
马勒测度是马勒在数论研究中引入的。众所周知，马勒测度出现在数学和物理的不同领域。另一方面，通过我们之前关于“Zeta 对应”的一系列工作，我们研究了一类新的 zeta 函数，用于包括量子行走在内的各种行走。量子游走是随机游走的量子对应。在本文中，我们提出了马勒测度和量子行走的 zeta 函数之间的新关系。首先，我们在一维量子行走的情况下考虑这种关系。然后我们处理高维量子行走。为了与量子游走的情况进行比较，我们还处理高维随机游走的情况。我们的结果首次通过量子行走在马勒测度和 zeta 函数之间建立了桥梁。
The Mahler measure was introduced by Mahler in the study of number theory. It is known that the Mahler measure appears in different areas of mathematics and physics. On the other hand, we have been investigated a new class of zeta functions for various kinds of walks including quantum walks by a series of our previous work on “Zeta Correspondence”. The quantum walk is a quantum counterpart of the random walk. In this paper, we present a new relation between the Mahler measure and our zeta function for quantum walks. Firstly we consider this relation in the case of one-dimensional quantum walks. Afterwards we deal with higher-dimensional quantum walks. For comparison with the case of the quantum walk, we also treat the case of higher-dimensional random walks. Our results bridge between the Mahler measure and the zeta function via quantum walks for the first time.