On the vanishing order of Jacobi forms at infinity

Key Points

• The study aims to establish upper bounds on the vanishing order of Jacobi forms, both classical and of lattice index.
• Defined two types of upper bounds for vanishing order of Jacobi forms at infinity.
• Analyzed classical Jacobi forms and those with lattice index.
• Derived a lower bound on the slope of orthogonal modular forms.
• Established optimal upper bounds for classical Jacobi forms.
• Proved that the module of symmetric formal Fourier–Jacobi series has finite rank.
• Demonstrated lower bound implications for orthogonal modular forms.