Theta Blocks
Number Theory
2019-07-02 v1
Abstract
We define theta blocks as products of Jacobi theta functions divided by powers of the Dedekind eta-function and show that they give a powerful new method to construct Jacobi forms and Siegel modular forms, with applications also in lattice theory and algebraic geometry. One of the central questions is when a theta block defines a Jacobi form. It turns out that this seemingly simple question is connected to various deep problems in different fields ranging from Fourier analysis over infinite-dimensional Lie algebras to the theory of moduli spaces in algebraic geometry. We give several answers to this question.
Cite
@article{arxiv.1907.00188,
title = {Theta Blocks},
author = {Valery Gritsenko and Nils-Peter Skoruppa and Don Zagier},
journal= {arXiv preprint arXiv:1907.00188},
year = {2019}
}