On the proximity of multiplicative functions to the number of distinct prime factors function
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Jean-Marie De Koninck
,
Nicolas Doyon
Abstract
Given an additive function f and a multiplicative function g, let E(f, g;x) = #{n ≤ x: f(n) = g(n)}. We study the size of E(ω,g;x) and E(Ω,g;x), where ω(n) stands for the number of distinct prime factors of n and Ω(n) stands for the number of prime factors of n counting multiplicity. In particular, we show that E(ω,g;x) and E(Ω,g;x) are
The work of the first author was supported by a grant from NSERC.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Small-large subgroups of the reals
- Structural properties of algebras of S-probabilities
- Approximation in quantum measure spaces
- On Fibonomial sums identities with special sign functions: analytically q-calculus approach
- On the proximity of multiplicative functions to the number of distinct prime factors function
- Truncated euler polynomials
- Growth series of crossed and two-sided crossed products of cyclic groups
- Weakly U-abundant semigroups with strong Ehresmann transversals
- Iterative learning control with pulse compensation for fractional differential systems
- Rectifiable and nonrectifiable solution curves of half-linear differential systems
- Uniqueness properties of meromorphic functions in the light of three shared sets
- A new family of analytic functions defined by means of Rodrigues type formula
- Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
- On the solutions of a second-order difference equation in terms of generalized Padovan sequences
- Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
- A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation
- Productively sequential spaces
- Euler classes of vector bundles over iterated suspensions of real projective spaces
- The stationary distribution and ergodicity of a stochastic mutualism model
- Restricted injective dimensions over local homomorphisms
