Simple lattices and free algebras of modular forms

DOI10.1016/j.aim.2022.108835OpenAlexW4313334479MaRDI QIDQ2679891

Brandon Williams, Haowu Wang

Publication date: 26 January 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.13343

zbMATH Keywords

reflection groupsBorcherds productssimple latticessymmetric domains of type IVmodular forms on orthogonal groups

Mathematics Subject Classification ID

Relationship to Lie algebras and finite simple groups (11F22) Other groups and their modular and automorphic forms (several variables) (11F55) Reflection groups, reflection geometries (51F15) Automorphic functions in symmetric domains (32N15)

Related Items (2)

Automorphic products that are singular modulo primes ⋮ Fano Shimura varieties with mostly branched cusps

Uses Software

• SageMath
• sfqm

Cites Work

• Unnamed Item
• Unnamed Item
• On the converse theorem for Borcherds products
• Some free algebras of automorphic forms on symmetric domains of type IV
• Hermitian modular forms and the Burkhardt quartic
• Automorphic forms with singularities on Grassmannians
• Graded rings of Hermitian modular forms of degree 2
• Some modular varieties of low dimension
• Borcherds products on \(O(2,l)\) and Chern classes of Heegner divisors
• Poincaré square series for the Weil representation
• The Gross-Kohnen-Zagier theorem in higher dimensions
• On some free algebras of orthogonal modular forms. II
• On some free algebras of orthogonal modular forms
• A construction of antisymmetric modular forms for Weil representations
• On some free algebras of automorphic forms
• A criterion of smoothness at infinity for an arithmetic quotient of the future tube
• On the classification of automorphic products and generalized Kac-Moody algebras
• Siegel modular forms of half integral weight and a lifting conjecture
• Automorphic products of singular weight for simple lattices
• Compactification of arithmetic quotients of bounded symmetric domains
• The graded ring of quaternionic modular forms of degree 2
• The graded ring of modular forms on the Cayley half-space of degree two
• Some modular varieties of low dimension. II
• Lattices with many Borcherds products
• Structure of the module of vector-valued modular forms
• Invariant Theory
• On Siegel modular forms. Part I.
• Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections
• SIMPLE GRADED RINGS OF SIEGEL MODULAR FORMS, DIFFERENTIAL OPERATORS AND BORCHERDS PRODUCTS
• The classification of free algebras of orthogonal modular forms
• The ring of modular forms for the even unimodular lattice of signature (2,10)
• Quasi‐pullback of Borcherds products
• Holomorphic Borcherds products of singular weight for simple lattices of arbitrary level
• On Siegel Modular Forms of Genus Two
• ON SIEGEL MODULAR VARIETIES OF LEVEL 3

This page was built for publication: Simple lattices and free algebras of modular forms