Antisymmetric paramodular forms of weight 3

Abstract

The problem on the construction of antisymmetric paramodular forms of canonical weight 3 was open since 1998. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer surfaces associated to $(1,t)$-polarised abelian surfaces. In this paper, we construct the first infinite family of antisymmetric paramodular forms of weight 3 as Borcherds products whose first Fourier-Jacobi coefficient is a theta block.

accepted for publication in Sbornik: Mathematics

References in corpus (1)

• Theta block conjecture for paramodular forms of weight 2

Cited by in corpus (3)

• The classification of 2-reflective modular forms
• Reflective modular forms on lattices of prime level
• Theta block conjecture for Siegel paramodular forms