18 citations · 80 across the 26 of their papers we have counts for
33 papers
Some applications of the moduli space of -polarized K3 surfaces
Adrian Clingher, Andreas Malmendier, Brandon Williams
We study K3 surfaces polarized by the lattice through elliptic fibrations and orthogonal modular forms. Using an alternate genus-one fibration and its relative Ja…
On the Vinberg Family of K3 Surfaces
Adrian Clingher, Andreas Malmendier, Brandon Williams
We study orthogonal modular forms associated with moduli spaces of lattice-polarized K3 surfaces whose generic transcendental lattices are of the form …
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 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…
Binary theta functions and Borcherds products
Markus Schwagenscheidt, Brandon Williams
We obtain infinite product expansions in the sense of Borcherds for theta functions associated with certain positive-definite binary quadratic and binary hermitian forms. Among oth…
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…