Valery Gritsenko, Nils-Peter Skoruppa, Don Zagier
Published 2019-06-29Version 1
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.
Orbits of Jacobi forms and Theta relations
Periods of modular forms on $Γ_0(N)$ and products of Jacobi theta functions
Short proofs for $q$-Raabe formula and integrals for Jacobi theta functions
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