Quadratic forms and their theta series - infinitesimal aspects

2011/06/24 by Juan Marcos Cerviño, Cerviño, Juan Marcos, Georg Hein +1
Mathematics · #11E45 #11F11 #11F27 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E45 #msc:11F11 #msc:11F27

paper · pdf · doi:10.48550/arxiv.1106.4895

11 pages

arxiv created 2011/06/24 · openalex publication_date 2011/06/24 · arxiv updated 2011/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the theta map which assigns to a real quadratic form its theta series. We introduce two invariants reflecting whether the differential of the theta map vanishes or is degenerate. We provide examples of lattices where this differential is zero. These invariants turn out to be modular forms for integral lattices. We illustrate this in the rank two case.

Citations

• Lattice invariants from the heat kernel (II)

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