Theta block conjecture for paramodular forms of weight 2

Abstract

In this paper we construct an infinite family of paramodular forms of weight $2$ which are simultaneously Borcherds products and additive Jacobi lifts. This proves an important part of the theta-block conjecture of Gritsenko--Poor--Yuen (2013) related to the only known infinite series of theta-blocks of weight $2$ and $q$-order $1$. We also consider some applications of this result.

Minor revision, accepted for publication in Proc. Amer. Math. Soc

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• Antisymmetric paramodular forms of weight 3