Affiliation:
1. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China
Abstract
Let [Formula: see text] be a positive integer, and define [Formula: see text] for [Formula: see text], where [Formula: see text] denotes the number of distinct prime factors of [Formula: see text], and [Formula: see text] represents the total number of prime factors of [Formula: see text] (counted with multiplicity). In this paper, we study these two zeta functions and related arithmetical functions. We show that [Formula: see text] which is similar to the known identity [Formula: see text] equivalent to the Prime Number Theorem. For [Formula: see text], we prove that [Formula: see text] We also raise a hypothesis on the parities of [Formula: see text] which implies the Riemann Hypothesis.
Funder
National Natural Science Foundation of China (CN)
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
1 articles.
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