18 citations · 78 across the 34 of their papers we have counts for
38 papers
Dynkin diagrams, generalized Nahm sums and 2d CFTs
Kaiwen Sun, Haowu Wang
A folklore conjecture states that the Nahm sum associated with a pair of Dynkin diagrams of type is a modular function. In this paper, we extend this conjecture to Dynkin di…
On the vanishing order of Jacobi forms at infinity
Jialin Li, Haowu Wang
In this paper, we establish two types of upper bounds on the vanishing order of Jacobi forms at infinity. The first type is for classical Jacobi forms, which is optimal in a certai…
Jacobi forms of weight one on
Jialin Li, Haowu Wang
Let be the vector space of Jacobi forms of weight one and index on . In 1985, Skoruppa proved that for all . In 2007, Ibukiyama and Skoru…
Sums of four polygonal numbers: precise formulas
Jialin Li, Haowu Wang
In this paper we give unified formulas for the numbers of representations of positive integers as sums of four generalized -gonal numbers, and as restricted sums of four squares…
On Intermediate Exceptional Series
Kimyeong Lee, Kaiwen Sun, Haowu Wang
The Freudenthal--Tits magic square for of semi-simple Lie algebras can be extende…
Orbits of Jacobi forms and Theta relations
Valery Gritsenko, Haowu Wang
Jacobi theta functions with rational characteristics can be viewed as vector-valued Jacobi forms. Theta relations usually correspond to different constructions of certain Jacobi fo…
Hyperbolization of Affine Lie Algebras
Kaiwen Sun, Haowu Wang, Brandon Williams
In 1983, Feingold and Frenkel discovered a relation between Siegel modular forms of genus two and a rank-three hyperbolic Kac--Moody algebra extending the affine Lie algebra of typ…
Automorphic products that are singular modulo primes
Haowu Wang, Brandon Williams
We use Rankin--Cohen brackets on O(n, 2) to prove that the Fourier coefficients of reflective Borcherds products often satisfy congruences modulo certain primes.
On intermediate Lie algebra
Kimyeong Lee, Kaiwen Sun, Haowu Wang
is an intermediate Lie algebra filling a hole between and in the Deligne-Cvitanović exceptional series. It was found independently by Mathur, Muhki, Sen in…
There are no extremal eutactic stars other than root systems
Haowu Wang
A eutactic star on an integral lattice is called extremal if it induces a holomorphic Jacobi form of lattice index and singular weight via the theta block. The famous Macdonald ide…
On the classification of reflective modular forms
Haowu Wang
A modular form on an even lattice of signature is called reflective if it vanishes only on quadratic divisors orthogonal to roots of . In this paper we show that eve…
-reflective lattices of signature with
Haowu Wang
An even lattice of signature is called -reflective if there is a non-constant modular form for the orthogonal group of which vanishes only on quadratic divisors…
On the non-existence of singular Borcherds products
Haowu Wang, Brandon Williams
Let and be a modular form of weight on which vanishes only on rational quadratic divisors. We prove that has only simple zeros and that…
Mathieu moonshine and Borcherds products
Haowu Wang, Brandon Williams
The twisted elliptic genera of a surface associated with the conjugacy classes of the Mathieu group are known to be weak Jacobi forms of weight . In 2010, Cheng co…
The fake monster algebra and singular Borcherds products
Haowu Wang, Brandon Williams
In this paper we consider several problems in the theory of automorphic products and generalized Kac--Moody algebras proposed by Borcherds in 1995. We show that the denominator of…
Modular forms with poles on hyperplane arrangements
Haowu Wang, Brandon Williams
We study algebras of meromorphic modular forms whose poles lie on Heegner divisors for orthogonal and unitary groups associated to root lattices. We give a uniform construction of…
Conway invariant Jacobi forms on the Leech lattice
Kaiwen Sun, Haowu Wang
In this paper we study Jacobi forms associated with the Leech lattice which are invariant under the Conway group . We determine and construct generators of modul…
Siegel modular forms of degree two and level five
Haowu Wang, Brandon Williams
We construct a ring of meromorphic Siegel modular forms of degree 2 and level 5, with singularities supported on an arrangement of Humbert surfaces, which is generated by four sing…
Weyl invariant Jacobi forms and -strings
Kaiwen Sun, Haowu Wang
In 1992 Wirthmüller showed that for any irreducible root system not of type the ring of weak Jacobi forms invariant under Weyl group is a polynomial algebra. However, it has…
Graded rings of Hermitian modular forms with singularities
Haowu Wang, Brandon Williams
We study graded rings of meromorphic Hermitian modular forms of degree two whose poles are supported on an arrangement of Heegner divisors. For the group $\mathrm{SU}_{2,2}(\mathca…
Free algebras of modular forms on ball quotients
Haowu Wang, Brandon Williams
In this paper we study algebras of modular forms on unitary groups of signature . We give a necessary and sufficient condition for an algebra of unitary modular forms to be…
On weak Jacobi forms of rank two
Haowu Wang, Brandon Williams
We study a ring of weak Jacobi forms indexed by integral lattices of rank two. We find an explicit finite set of generators of this ring and give a dimension formula for weak Jacob…
Simple lattices and free algebras of modular forms
Haowu Wang, Brandon Williams
We study the algebras of modular forms on type IV symmetric domains for simple lattices; that is, lattices for which every Heegner divisor occurs as the divisor of a Borcherds prod…
Projective spaces as orthogonal modular varieties
Haowu Wang, Brandon Williams
We construct reflection groups acting on symmetric domains of Cartan type IV, for which the graded algebras of modular forms are freely generated by forms of…