Irreducible polynomials in F_q[x] versus 1 - qz in C[z]
| dc.creator | Brent, Barry | |
| dc.date | 2006-12-20 | |
| dc.date | 2006-12-21 | |
| dc.date.accessioned | 2026-07-07T07:36:36Z | |
| dc.date.available | 2026-07-07T07:36:36Z | |
| dc.description | Let q be a prime power and N_n count degree-n monic irreducible polynomials in F_q[x]. We show that prod_{n=1}^{\infty} (1 -z^n)^N_n = 1 - qz for small |z|. | |
| dc.description | 2 pages. v.1 replaced because the proof of absolute convergence was valid only on reals. (It used l'Hopital.) Sadder news: "...you've simply rediscovered the Weil conjectures for P^1. ..." (email from Kevin Buzzard) | |
| dc.identifier | https://arxiv.org/abs/math/0612614 | |
| dc.identifier | http://arxiv.org/abs/math/0612614 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120486 | |
| dc.subject | Number Theory | |
| dc.subject | 11T99 | |
| dc.title | Irreducible polynomials in F_q[x] versus 1 - qz in C[z] | |
| dc.type | text |