Spherical designs and zeta functions of lattices
| dc.creator | Coulangeon, Renaud | |
| dc.date | 2006-11-23 | |
| dc.date | 2006-12-14 | |
| dc.date.accessioned | 2026-07-07T07:34:34Z | |
| dc.date.available | 2026-07-07T07:34:34Z | |
| dc.description | We set up a connection between the theory of spherical designs and the question of minima of Epstein's zeta function. More precisely, we prove that a Euclidean lattice, all layers of which hold a 4-design, achieves a local minimum of the Epstein's zeta function, at least at any real s>n/2. We deduce from this a new proof of Sarnak and Strömbergsson's theorem asserting that the root lattices D4 and E8, as well as the Leech lattice, achieve a strict local minimum of the Epstein's zeta function at any s>0. Furthermore, our criterion enables us to extend their theorem to all the so-called extremal modular lattices(up to certain restrictions) using a theorem of Bachoc and Venkov, and to other classical families of lattices (e.g. the Barnes-Wall lattices). | |
| dc.description | In this revised version, we added a section 4, about the minima of theta functions | |
| dc.identifier | https://arxiv.org/abs/math/0611735 | |
| dc.identifier | http://arxiv.org/abs/math/0611735 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119806 | |
| dc.subject | Number Theory | |
| dc.subject | 11H55 | |
| dc.title | Spherical designs and zeta functions of lattices | |
| dc.type | text |