论文标题
Mahler/Zeta对应
Mahler/Zeta Correspondence
论文作者
论文摘要
马勒（Mahler）在数字理论的研究中引入了马勒措施。众所周知，Mahler度量出现在数学和物理学的不同领域。另一方面，我们已经研究了一类新的Zeta功能，用于各种步行，包括量子步行，这是我们先前关于“ Zeta通信”的一系列工作。量子步行是随机步行的量子对应物。在本文中，我们提出了Mahler量度与我们的Zeta功能之间的新关系。首先，在一维量子步行的情况下，我们认为这种关系。之后，我们处理高维量子步行。为了与量子步行的情况进行比较，我们还可以处理更高维度随机步行的情况。我们的结果首次通过量子步道桥接了Mahler度量和Zeta功能。
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.
