G-functions and multisum versus holonomic sequences
| dc.creator | Garoufalidis, Stavros | |
| dc.date | 2007-08-31 | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:18Z | |
| dc.date.available | 2026-07-07T10:17:18Z | |
| dc.description | The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of $G$-functions that come from enumerative combinatorics, and (c) we give a counterexample to a question of Zeilberger that asks whether holonomic sequences can be written as multisums of balanced hypergeometric terms. The proofs utilize the notion of a $G$-function, introduced by Siegel, and its analytic/arithmetic properties shown recently by André. | |
| dc.description | 8 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0708.4354 | |
| dc.identifier | http://arxiv.org/abs/0708.4354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173808 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 57N10, 57M25 | |
| dc.title | G-functions and multisum versus holonomic sequences | |
| dc.type | text |