On some free algebras of orthogonal modular forms II

Haowu Wang

paper

On some free algebras of orthogonal modular forms II

arXiv:2006.02680

Abstract

In this paper we construct 16 free algebras of modular forms on symmetric domains of type IV for some reflection groups related to the eight lattices $A_{1} (2)$ , $A_{1} (3)$ , $A_{1} (4)$ , $2 A_{1} (2)$ , $A_{2} (2)$ , $A_{2} (3)$ , $A_{3} (2)$ , $D_{4} (2)$ . As a corollary, we prove the modularity of formal Fourier--Jacobi expansions for these reflection groups.

arXiv commentRevised version, to appear in Research in Number Theory