Lattice invariants from the heat kernel

Details Lattice invariants from the heat kernel Lattice invariants from the heat kernel

2009-06-05

arxiv.org/abs/0906.1128v1

Mathematics

Number Theory

12 pages

Scientific paper

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 $\Theta_{nn,\Lambda}$
depend only from lengths and angles in the lattice.

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