Modular forms of orthogonal type and Jacobi theta-series
Algebraic Geometry
2011-06-24 v1 Number Theory
Abstract
In this paper we consider Jacobi forms of half-integral index for any positive definite lattice L (classical Jacobi forms from the book of Eichler and Zagier correspond to the lattice A_1=<2>). We give a lot of examples of Jacobi forms of singular and critical weights for root systems using Jacobi theta-series. We describe the Jacobi lifting for Jacobi forms of half-integral indices. In some case it gives additive lifting construction of new reflective modular forms.
Keywords
Cite
@article{arxiv.1106.4733,
title = {Modular forms of orthogonal type and Jacobi theta-series},
author = {Fabien Clery and Valery Gritsenko},
journal= {arXiv preprint arXiv:1106.4733},
year = {2011}
}
Comments
28 pages