Arrangements of hyperplanes II: Szenes formula and Eisenstein series
| dc.creator | Brion, Michel | |
| dc.creator | Vergne, Michele | |
| dc.date | 1999-03-30 | |
| dc.date | 1999-10-12 | |
| dc.date.accessioned | 2026-07-07T05:28:33Z | |
| dc.date.available | 2026-07-07T05:28:33Z | |
| dc.description | The aim of this article is to generalize in several variables some formulae for Eisenstein series in one variable. For example the formula $2ζ(2k) = (2π)^{2k} \frac{B_{2k}}{(2k)!} = Res_{z=0}(\frac{1}{z^{2k}(1-e^z)})$ for the values of zeta functions at even integers in functions of Bernoulli numbers. A. Szenes proved in several variables a similar residue formula for the values of the zeta function introduced by Witten. We introduce some Eisenstein series by averaging over a lattice rational functions with poles in an arrangement of hyperplanes. We give another proof of Szenes residue formula by relating it to the constant term of these Eisenstein series. | |
| dc.description | revised version (introduction rewritten, references added, minor changes made), 28 pages, LaTEX2e | |
| dc.identifier | https://arxiv.org/abs/math/9903180 | |
| dc.identifier | http://arxiv.org/abs/math/9903180 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78296 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 52B30; 40B05; 11B68 | |
| dc.title | Arrangements of hyperplanes II: Szenes formula and Eisenstein series | |
| dc.type | text |