The expected number of zeros of a random system of $p$-adic polynomials
| dc.creator | Evans, Steven N. | |
| dc.date | 2006-02-21 | |
| dc.date | 2006-10-06 | |
| dc.date.accessioned | 2026-07-07T07:03:40Z | |
| dc.date.available | 2026-07-07T07:03:40Z | |
| dc.description | We study the simultaneous zeros of a random family of $d$ polynomials in $d$ variables over the $p$-adic numbers. For a family of natural models, we obtain an explicit constant for the expected number of zeros that lie in the $d$-fold Cartesian product of the $p$-adic integers. Considering models in which the maximum degree that each variable appears is $N$, this expected value is \[ p^{d \lfloor \log_p N \rfloor} (1 + p^{-1} + p^{-2} + ... + p^{-d})^{-1} \] for the simplest such model. | |
| dc.description | 13 pages, no figures, revised to incorporate referees' comments | |
| dc.identifier | https://arxiv.org/abs/math/0602478 | |
| dc.identifier | http://arxiv.org/abs/math/0602478 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109061 | |
| dc.subject | Probability | |
| dc.subject | Commutative Algebra | |
| dc.subject | 60B99; 30G15; 11S80; 30G06 | |
| dc.title | The expected number of zeros of a random system of $p$-adic polynomials | |
| dc.type | text |