Lucas-type congruences for cyclotomic $ψ$-coefficients
| dc.creator | Sun, Zhi-Wei | |
| dc.creator | Wan, Daqing | |
| dc.date | 2005-12-01 | |
| dc.date | 2008-04-17 | |
| dc.date.accessioned | 2026-07-07T09:33:00Z | |
| dc.date.available | 2026-07-07T09:33:00Z | |
| dc.description | Let p be any prime and a be a positive integer. For nonnegative integers l,n and an integer r, the normalized cyclotomic $ψ$-coefficient $${n,r}_{l,p^a}:=p^{-[(n-p^{a-1}-lp^a)/(p^{a-1}(p-1))]} \sum_{k=r(mod p^a)}(-1)^k{n \choose k}{{(k-r)/p^a} \choose l}$$ is known to be an integer. In this paper, we show that this coefficient behaves like binomial coefficients and satisfies some Lucas-type congruences. This implies that a congruence of Wan is often optimal, and two conjectures of Sun and Davis are true. | |
| dc.identifier | https://arxiv.org/abs/math/0512012 | |
| dc.identifier | http://arxiv.org/abs/math/0512012 | |
| dc.identifier | Int. J. Number Theory 4(2008), no.2, 155--170 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158987 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B65; 05A10; 11A07; 11R18; 11R23; 11S05 | |
| dc.title | Lucas-type congruences for cyclotomic $ψ$-coefficients | |
| dc.type | text |