Asymptotic density of Catalan numbers modulo 3 and powers of 2
Rob Burns
TL;DR
This paper investigates the distribution of Catalan numbers when taken modulo 3 and powers of 2, providing insights into their asymptotic density and behavior in modular arithmetic.
Contribution
It determines the asymptotic density of Catalan numbers modulo 3 and powers of 2, a novel analysis in the context of combinatorial number theory.
Findings
Catalan numbers have a specific asymptotic density modulo 3.
Catalan numbers exhibit particular distribution patterns modulo powers of 2.
The results enhance understanding of Catalan numbers in modular arithmetic contexts.
Abstract
We establish the asymptotic density of the Catalan numbers modulo 3 and modulo powers of 2.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Meromorphic and Entire Functions