Congruences of the partition function
| dc.creator | Yang, Yifan | |
| dc.date | 2009-04-16 | |
| dc.date.accessioned | 2026-07-07T13:05:05Z | |
| dc.date.available | 2026-07-07T13:05:05Z | |
| dc.description | Let $p(n)$ denote the partition function. In this article, we will show that congruences of the form $$ p(m^j\ell^kn+B)\equiv 0\mod m \text{for all} n\ge 0 $$ exist for all primes $m$ and $\ell$ satisfying $m\ge 13$ and $\ell\neq 2,3,m$. Here the integer $k$ depends on the Hecke eigenvalues of a certain invariant subspace of $S_{m/2-1}(Γ_0(576),χ_{12})$ and can be explicitly computed. More generally, we will show that for each integer $i>0$ there exists an integer $k$ such that for every non-negative integers $j\ge i$ with a properly chosen $B$ the congruence $$ p(m^j\ell^kn+B)\equiv 0\mod m^i $$ holds for all integers $n$ not divisible by $\ell$. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0904.2530 | |
| dc.identifier | http://arxiv.org/abs/0904.2530 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227383 | |
| dc.subject | Number Theory | |
| dc.subject | 11P83; 11F25, 11F37, 11P82 | |
| dc.title | Congruences of the partition function | |
| dc.type | text |