Lattice invariants from the heat kernel (II)

Abstract

Given an integral lattice $\Lambda$ of rank $n$ and a finite sequence $m_1\le m_2\le ...\le m_k$ of natural numbers we construct a modular form ${\Theta }_{m_1,m_2,...,m_k,\Lambda }$ of level $N=N(\Lambda )$. The weight of this modular form is $nk/2+{\sum }_{i=1}^k{m}_k$. This construction generalizes the theta series ${\Theta }_{\Lambda }$ of integral lattices, because ${\Theta }_{\Lambda }={\Theta }_{0,\Lambda }$. We give the $q$-expansions of the modular forms ${\Theta }_{m,m,\Lambda }$, and ${\Theta }_{1,1,1,\Lambda }$ and show that (up to some scaling) they are given by power series with integer coefficients.

12 pages, continuation of arXiv:0906.1128

Cited by in corpus (1)

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