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Asymptotic $\psi$-densities of subsets of natural numbers
- Publication Year :
- 2024
-
Abstract
- The sizes of subsets of the natural numbers are typically quantified in terms of asymptotic (linear) and logarithmic densities. These concepts have been generalized to weighted $w$-densities, where a specific weight function $w$ plays a key role. In this paper, a parallel theory of asymptotic $\psi$-densities is introduced, where the weight is expressed slightly differently in terms of differentiable functions $\psi$, which are either concave or convex and satisfy certain asymptotic properties. Alternative new proofs for known results on analytic and Abel densities are also given.<br />Comment: 27 pages
- Subjects :
- Mathematics - Classical Analysis and ODEs
Mathematics - Complex Variables
11B05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.07600
- Document Type :
- Working Paper