Explicit linear dependence congruence relations for the partition function modulo 4

Autor:	Charlton, Steven
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Primary: 11P83. Secondary: 05A17
Druh dokumentu:	Working Paper
Popis:	Almost nothing is known about the parity of the partition function $p(n)$, which is conjectured to be random. Despite this expectation, Ono surprisingly proved the existence of infinitely many linear dependence congruence relations modulo 4 for $p(n)$, indicating that the parity of the partition function cannot be truly random. Answering a question of Ono, we explicitly exhibit the first examples of these relations which he proved theoretically exist. The first two relations invoke 131 (resp. 198) different discriminants $D \leq 24k-1$ for $k=309$ (resp. $k=312$); new relations occur for $k = 316, 317, 319, 321, 322, 326, \ldots$. Comment: 11 pages, code attached
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.17459 Zobrazit plný text záznamu View this record from Arxiv