Some remarks on a paper of V. A. Liskovets
L\'aszl\'o T\'oth
TL;DR
This paper explores properties of the orbicyclic function E, its connections to linear congruences, and related functions, providing new insights and simple proofs within number theory and analytic properties of zeta functions.
Contribution
It introduces new properties of the orbicyclic function E and clarifies its relation to existing literature and functions studied by other researchers.
Findings
New properties of the orbicyclic function E
Connections between E and solutions to linear congruences
Number theoretic proofs of known properties
Abstract
We deduce new properties of the orbicyclic function of several variables investigated in a recent paper by V. A. Liskovets. We point out that the function and its connection to the number of solutions of certain linear congruences occur in the literature in a slightly different form. We investigate another similar function considered by Deitmar, Koyama and Kurokawa by studying analytic properties of some zeta functions of Igusa type. Simple number theoretic proofs for some known properties are also given.
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