Zeta functions of periodic cubical lattices and cyclotomic-like polynomials.
Zeta functions of periodic cubical lattices and cyclotomic-like polynomials.
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周期性立方晶格和分圆多项式的 Zeta 函数。
DOI：
10.2969/aspm/08410093
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
T. Shirai
中科院分区：
文献类型：
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作者：
Y. Hiraoka;Hiroyuki Ochiai;T. Shirai
周期立方晶格的 Zeta 函数是通过计算邻接算子的所有特征值及其特征多项式显式导出的。我们引入类分圆多项式来对 zeta 函数进行因式分解，并计算与每个分圆多项式相关的伽罗瓦作用的轨道数，以获得其进一步的因式分解。我们还给出了这样一个多项式不可约的充要条件，并从这个角度讨论了它的不可约性。
Zeta functions of periodic cubical lattices are explicitly derived by computing all the eigenvalues of the adjacency operators and their characteristic polynomials. We introduce cyclotomic-like polynomials to give factorization of the zeta function in terms of them and count the number of orbits of the Galois action associated with each cyclotomic-like polynomial to obtain its further factorization. We also give a necessary and sufficient condition for such a polynomial to be irreducible and discuss its irreducibility from this point of view.