Spherical designs and zeta functions of lattices
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COULANGEON, Renaud | |
| dc.date.accessioned | 2024-04-04T03:04:07Z | |
| dc.date.available | 2024-04-04T03:04:07Z | |
| dc.date.created | 2006-12-14 | |
| dc.date.issued | 2006 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193122 | |
| dc.description.abstractEn | 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.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | Spherical designs and zeta functions of lattices | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | math/0611735 | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.page | Art. ID 49620, 16 pp. | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00192934 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00192934v1 | |
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