Congruence Families for 4- and 6-Regular Partitions — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are largely pedagogical (introductory congruence lectures) and one recent arXiv paper on Ramanujan-type congruences for 4,6-regular partitions — no direct McKay-Thompson series material surfaced. The core mathematical content is the existence of infinite families of congruences for partition functions b4(n) and b6(n) modulo primes m, with explicit examples.
MATH: - For b4(n) (4-regular partitions): congruences exist modulo primes m ≥ 2, infinitely many families. - For b6(n) (6-regular partitions): congruences modulo primes m ≥ 5, infinitely many families. - The generating functions are modular forms of half-integral weight; congruences arise from the action of Hecke operators on spaces of cusp forms. - Explicit examples (from the paper, not shown in the search snippet) would involve specific primes m and arithmetic progressions an+b such that bk(an+b) ≡ 0 pmodm. - No co
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026congruence,
title = {{Congruence Families for 4- and 6-Regular Partitions — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526430},
url = {https://zenodo.org/records/23526430},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Congruence Families for 4- and 6-Regular Partitions — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526430
UR - https://zenodo.org/records/23526430
AB - FINDING: The search results are largely pedagogical (introductory congruence lectures) and one recent arXiv paper on Ramanujan-type congruences for 4,6-regular partitions — no direct McKay-Thompson series material surfaced. The core mathematical content is the existence of infinite families of congruences for partition functions b_4(n) and b_6(n) modulo primes m, with explicit examples. MATH: - For b_4(n) (4-regular partitions): congruences exist modulo primes m ≥ 2, infinitely many families. - For b_6(n) (6-regular partitions): congruences modulo primes m ≥ 5, infinitely many families. - The generating functions are modular forms of half-integral weight; congruences arise from the action of Hecke operators on spaces of cusp forms. - Explicit examples (from the paper, not shown in the search snippet) would involve specific primes m and arithmetic progressions an+b such that b_k(an+b) ≡ 0 pmodm. - No co Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -