论文标题
迈向二分法用于雷德齐塔功能
Towards a dichotomy for the Reidemeister zeta function
论文作者
论文摘要
我们证明了理性和自然边界之间的二分法，用于reidemeister zeta函数的分析行为，用于非最有限产生的扭转型阿伯利亚群体的自形和$ \ mathbb z_p^d组的内态形态，$ \ mathbb z_p^d，$ \ mathbb z_p z_p z_p z_p z_p $ the p-padic integers of p-dadic integers。结果，我们获得了拓扑空间的连续图的二分法，其基本群是非最初产生的扭转型阿伯利亚人组。我们还基于弱的交换性条件，证明了巧合reidemister zeta函数的合理性Zeta Zeta函数对有限生成的无扭转的尼尔氏群体的合理性。
We prove a dichotomy between rationality and a natural boundary for the analytic behavior of the Reidemeister zeta function for automorphisms of non-finitely generated torsion abelian groups and for endomorphisms of groups $\mathbb Z_p^d,$ where $\mathbb Z_p$ the group of p-adic integers. As a consequence, we obtain a dichotomy for the Reidemeister zeta function of a continuous map of a topological space with fundamental group that is non-finitely generated torsion abelian group. We also prove the rationality of the coincidence Reidemeister zeta function for tame endomorphisms pairs of finitely generated torsion-free nilpotent groups, based on a weak commutativity condition.
