论文标题
周期性立方晶格和循环样式多项式的Zeta功能
Zeta functions of periodic cubical lattices and cyclotomic-like polynomials
论文作者
论文摘要
通过计算邻接运算符及其特征多项式的所有特征值，可以明确得出周期性立方格的Zeta函数。我们介绍了类似环细胞的多项式，以将Zeta函数分解为它们，并计算与每个环形细胞样多项式相关的Galois动作轨道数量，以获得其进一步的分解。我们还提供了必要和充分的条件，使这种多项式是不可还原的，并从这个角度讨论了其不可约性。
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.
