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Spherical Designs and Heights of Euclidean Lattices
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COULANGEON, Renaud | |
| dc.contributor.author | LAZZARINI, Giovanni | |
| dc.date.accessioned | 2024-04-04T02:18:22Z | |
| dc.date.available | 2024-04-04T02:18:22Z | |
| dc.date.created | 2014-01-13 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0022-314X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189307 | |
| dc.description.abstractEn | We study the connection between the theory of spherical designs and the question of extrema of the height function of lattices. More precisely, we show that a full-rank n-dimensional Euclidean lattice, all layers of which hold a spherical 2-design, realises a stationary point for the height function, which is defined as the first derivative at 0 of the spectral zeta function of the associated flat torus. Moreover, in order to find out the lattices for which this 2-design property holds, a strategy is described which makes use of theta functions with spherical coefficients, viewed as elements of some space of modular forms. Explicit computations in dimension up to 7, performed with Pari/GP and Magma, are reported. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Spherical Designs and Heights of Euclidean Lattices | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jnt.2014.02.015 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1401.2891 | |
| bordeaux.journal | Journal of Number Theory | |
| bordeaux.page | 288-315 | |
| bordeaux.volume | 141 | |
| 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-00984174 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00984174v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Number%20Theory&rft.date=2014&rft.volume=141&rft.spage=288-315&rft.epage=288-315&rft.eissn=0022-314X&rft.issn=0022-314X&rft.au=COULANGEON,%20Renaud&LAZZARINI,%20Giovanni&rft.genre=article |
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