MacMahonesque partition functions detect sets related to primes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917894424625152 |
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| author | Gomez, Kevin |
| author_facet | Gomez, Kevin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MacMahonesque partition functions detect sets related to primes Gomez, Kevin Number Theory 11P81, 05A17 (Primary) 11Fxx (Secondary) 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. |
| title | MacMahonesque partition functions detect sets related to primes |
| topic | Number Theory 11P81, 05A17 (Primary) 11Fxx (Secondary) |
| url | https://arxiv.org/abs/2409.14253 |