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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCOULANGEON, Renaud
dc.contributor.authorLAZZARINI, Giovanni
dc.date.accessioned2024-04-04T02:18:22Z
dc.date.available2024-04-04T02:18:22Z
dc.date.created2014-01-13
dc.date.issued2014
dc.identifier.issn0022-314X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189307
dc.description.abstractEnWe 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.isoen
dc.publisherElsevier
dc.title.enSpherical Designs and Heights of Euclidean Lattices
dc.typeArticle de revue
dc.identifier.doi10.1016/j.jnt.2014.02.015
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1401.2891
bordeaux.journalJournal of Number Theory
bordeaux.page288-315
bordeaux.volume141
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00984174
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00984174v1
bordeaux.COinSctx_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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