Haowu Wang

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20222024

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math.NT2023

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.

math.NT2023

On the classification of reflective modular forms

Haowu Wang

A modular form on an even lattice $M$ of signature $(l, 2)$ is called reflective if it vanishes only on quadratic divisors orthogonal to roots of $M$ . In this paper we show that eve…

math.NT2023

$2$ -reflective lattices of signature $(n, 2)$ with $n \geq 8$

Haowu Wang

An even lattice $M$ of signature $(n, 2)$ is called $2$ -reflective if there is a non-constant modular form for the orthogonal group of $M$ which vanishes only on quadratic divisors…

math.NT2022

Mathieu moonshine and Borcherds products

Haowu Wang, Brandon Williams

The twisted elliptic genera of a $K 3$ surface associated with the conjugacy classes of the Mathieu group $M_{24}$ are known to be weak Jacobi forms of weight $0$ . In 2010, Cheng co…

Automorphic products that are singular modulo primes

On the classification of reflective modular forms

2-reflective lattices of signature (n,2) with n≥8

Mathieu moonshine and Borcherds products

$2$ -reflective lattices of signature $(n, 2)$ with $n \geq 8$