MacMahonesque partition functions detect sets related to primes
Number Theory
2025-01-20 v3
Abstract
Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are infinitely many such expressions in these functions. Here, we show how to modify and adapt their construction to detect cubes of primes as well as primes in arithmetic progressions.
Cite
@article{arxiv.2409.14253,
title = {MacMahonesque partition functions detect sets related to primes},
author = {Kevin Gomez},
journal= {arXiv preprint arXiv:2409.14253},
year = {2025}
}
Comments
Minor corrections caught by referee