Brandon Williams

activity

20172026

most citedOn some free algebras of orthogonal modular forms

18 citations · 80 across the 26 of their papers we have counts for

collaborators

Showing 2020Show all

6 papers · 1 filter

math.NT2020★ 3 cited

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…

math.NT2020★ 4 cited

Projective spaces as orthogonal modular varieties

Haowu Wang, Brandon Williams

We construct $16$ reflection groups $Γ$ acting on symmetric domains $D$ of Cartan type IV, for which the graded algebras of modular forms are freely generated by forms of…

math.NT2020★ 1 cited

Borcherds products of half-integral weight

Haowu Wang, Brandon Williams

We give a necessary and sufficient criterion for the existence of Borcherds products of half-integral weight associated to even lattices that split two hyperbolic planes. In partic…

math.NT2020

On some free algebras of orthogonal modular forms II

Haowu Wang

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 $A_{1} (2)$ , $A_{1} (3)$ , $A_{1} (4)$ ,…

math.NT2020★ 18 cited

On some free algebras of orthogonal modular forms

Haowu Wang, Brandon Williams

For 25 orthogonal groups of signature $(2, n)$ related to the root lattices $A_{1}$ , $2 A_{1}$ , $3 A_{1}$ , $4 A_{1}$ , $A_{2}$ , $A_{3}$ , $A_{4}$ , $A_{5}$ , $A_{6}$ , $A_{7}$ , $D_{4}$ , $D_{5}$ , $D_{6}$ , $D_{7}$ , $D_8…

math.NT2020

Two graded rings of Hermitian modular forms

Brandon Williams

We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in $Q (- 7)$ and $Q (- 11)$ . I…