{"paper":{"title":"Spherical Designs and Heights of Euclidean Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Lazzarini, Renaud Coulangeon","submitted_at":"2014-01-13T16:07:44Z","abstract_excerpt":"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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2891","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}