Hermitian modular forms and algebraic modular forms on SO(6)

2025/05/29 by Ibukiyama, Tomoyoshi, Williams, Brandon
#11F55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.23497

Abstract

We state conjectures that relate Hermitian modular forms of degree two and algebraic modular forms for the compact group SO(6). We provide evidence for these conjectures in the form of dimension formulas and explicit computations of eigenforms.

Citations

• The basis problem for modular forms for the Weil representation
• Definite orthogonal modular forms: Computations, Excursions and Discoveries
• Modular forms with poles on hyperplane arrangements
• Quinary forms and paramodular forms
• Global liftings between inner forms of GSp(4)
• On weak Jacobi forms of rank two
• Two graded rings of Hermitian modular forms
• Lattice methods for algebraic modular forms on classical groups
• The Hirzebruch-Mumford volume for the orthogonal group and applications
• On Borcherds products associated with lattices of prime discriminant

Related

• Two graded rings of Hermitian modular forms
• Congruences for Hermitan modular forms of degree 2
• On the computation of algebraic modular forms on compact inner forms of GSp₄
• Modular forms on indefinite orthogonal groups of rank three
• Quinary forms and paramodular forms