Arithmetic density and congruences of $\ell$-regular bipartitions
Nabin Kumar Meher, Ankita Jindal

TL;DR
This paper investigates divisibility properties and congruences of $ ext{ell}$-regular bipartition functions, providing new theoretical results and algorithms for congruences using modular forms and number theory techniques.
Contribution
It establishes almost divisibility conditions for $B_ ext{ell}(n)$ and develops an algorithm to find congruences for $B_p(n)$ using advanced modular form methods.
Findings
Proves almost divisibility of $B_ ext{ell}(n)$ by prime powers under certain conditions.
Derives infinite families of congruences for $B_3(n)$ and $B_5(n)$.
Provides an algorithm to generate congruences for $B_p(n)$ for prime $p$.
Abstract
Let denote the number of -regular bipartitions of In this article, we prove that is always almost divisible by if where is a fixed positive integer and where are prime numbers Further, we obtain an infinities families of congruences for and by using Hecke eigen form theory and a result of Newman \cite{Newmann1959}. Furthermore, by applying Radu and Seller's approach, we obtain an algorithm from which we get several congruences for , where is a prime number.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · semigroups and automata theory
