Reidemeister zeta函数的二分法
Towards a dichotomy for the Reidemeister zeta function
摘要：
我们证明了一个二分法之间的合理性和自然边界的Reidemeister zeta函数的分析行为的自同构的非生成扭阿贝尔群和自同态的群体$\mathbb Z_p^d,$其中$\mathbb Z_p$的p进整数。由此，我们得到了拓扑空间中基本群为非生成挠阿贝尔群的连续映射的Reidemeisterzeta函数的二分法.在弱交换性条件下，证明了无挠生成幂零群的驯服自同态对的重合Reidemeisterzeta函数的合理性.
英文摘要：
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.
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