Exponential Sums and Congruences with Factorials
| dc.creator | Garaev, Moubariz Z. | |
| dc.creator | Luca, Florian | |
| dc.creator | Shparlinski, Igor E. | |
| dc.date | 2004-03-24 | |
| dc.date.accessioned | 2026-07-07T05:06:43Z | |
| dc.date.available | 2026-07-07T05:06:43Z | |
| dc.description | We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials $n!m!$ and also derive asymptotic formulas for the number of solutions of various congruences with factorials. For example, we prove that the products of two factorials $n!m!$ with $\max\{n,m\}<p^{1/2+ε}$ are uniformly distributed modulo $p$, and that any residue class modulo $p$ is representable in the form $m!n!+n_1! + ... +n_{49}!$ with $\max \{m,n, n_1, >..., n_{49}\} < p^{8775/8794+ ε}$. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403424 | |
| dc.identifier | http://arxiv.org/abs/math/0403424 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70583 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11A07, 11B65, 11L40 | |
| dc.title | Exponential Sums and Congruences with Factorials | |
| dc.type | text |