Ramanujan congruences for a class of eta quotients
| dc.creator | Sinick, Jonah | |
| dc.date | 2008-10-10 | |
| dc.date | 2009-04-24 | |
| dc.date.accessioned | 2026-07-07T13:07:36Z | |
| dc.date.available | 2026-07-07T13:07:36Z | |
| dc.description | We consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes $\ell$ for which their coefficients $c(n)$ obey congruences of the form $c(\ell n + a) \equiv 0 \pmod \ell$. We apply this result to obtain a complete characterization of the congruences of the same form that the sequences $c_N(n)$ satisfy, where $c_N(n)$ is defined by $ \sum_{n=0}^{\infty} c_N(n)q^n = \prod_{n=1}^{\infty} \frac{1}{(1-q^n)(1-q^{Nn})}$. This last result answers a question of H.-C. Chan. | |
| dc.description | 12 pages. V2: Minor typographical and mathematical corrections | |
| dc.identifier | https://arxiv.org/abs/0810.1931 | |
| dc.identifier | http://arxiv.org/abs/0810.1931 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228140 | |
| dc.subject | Number Theory | |
| dc.subject | 11P83 | |
| dc.title | Ramanujan congruences for a class of eta quotients | |
| dc.type | text |