Theta Blocks

2019/06/29 by Valery Gritsenko, Gritsenko, Valery, Nils-Peter Skoruppa +3 · 1 citation
Mathematics · #11F50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1907.00188

openalex publication_date 2019/06/29 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

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.

Cited by

• On the vanishing order of Jacobi forms at infinity

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