p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation
| dc.creator | Furusho, Hidekazu | |
| dc.date | 2003-04-07 | |
| dc.date | 2003-09-28 | |
| dc.date.accessioned | 2026-07-07T04:56:40Z | |
| dc.date.available | 2026-07-07T04:56:40Z | |
| dc.description | Our main aim in this paper is to give a foundation of the theory of $p$-adic multiple zeta values. We introduce (one variable) $p$-adic multiple polylogarithms by Coleman's $p$-adic iterated integration theory. We define $p$-adic multiple zeta values to be special values of $p$-adic multiple polylogarithms. We consider the (formal) $p$-adic KZ equation and introduce the $p$-adic Drinfel'd associator by using certain two fundamental solutions of the $p$-adic KZ equation. We show that our $p$-adic multiple polylogarithms appear as coefficients of a certain fundamental solution of the $p$-adic KZ equation and our $p$-adic multiple zeta values appear as coefficients of the $p$-adic Drinfel'd associator. We show various properties of $p$-adic multiple zeta values, which are sometimes analogous to the complex case and are sometimes peculiar to the $p$-adic case, via the $p$-adic KZ equation. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304085 | |
| dc.identifier | http://arxiv.org/abs/math/0304085 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67005 | |
| dc.subject | Number Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 11S80,33B30 | |
| dc.title | p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation | |
| dc.type | text |