Lattice invariants from the heat kernel (II)

Details Lattice invariants from the heat kernel (II) Lattice invariants from the heat kernel (II)

2009-09-02

arxiv.org/abs/0909.0340v1

Mathematics

Number Theory

12 pages, continuation of arXiv:0906.1128

Scientific paper

Given an integral lattice $\Lambda$ of rank $n$ and a finite sequence $m_1 \leq m_2 \leq ... \leq m_k$ 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.

Affiliated with

Also associated with

No associations

Rating

Lattice invariants from the heat kernel (II) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lattice invariants from the heat kernel (II), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lattice invariants from the heat kernel (II) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-12066