Lattice invariants from the heat kernel

2009/06/05 by Juan Marcos Cerviño, Cerviño, Juan Marcos, Georg Hein +1 · 1 citation
Mathematics · #11E45 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E45

paper · pdf · doi:10.48550/arxiv.0906.1128

12 pages

arxiv created 2009/06/05 · arxiv updated 2009/12/01

Abstract

We derive lattice invariants from the heat flux of a lattice. Using systems of harmonic polynomials, we obtain sums of products of spherical theta functions which give new invariants of integer lattices which are modular forms. In particular, we show that the modular forms Θ_nn,Λ depend only from lengths and angles in the lattice.

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• Lattice invariants from the heat kernel (II)

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