Antisymmetric paramodular forms of weight 3

2019/06/24 by Gritsenko, Valery, Wang, Haowu
#11F27 #11F30 #11F46 #11F50 #11F55 #14K25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1906.09869

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.

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