All Questions

Suppose we have a $4 \times 6$ matrix $A$ of rank $4$ whose entries are rational numbers. Define $$ V = \{x \in \mathbb R^6 \mid A \cdot x = 0\} $$ and $$ \Lambda = \{x \in \mathbb Z^6 \mid A \cdot ...

Suppose we have two rank $n-1$ matrices in $\Bbb Z^{(n-1)\times n}$ given by $$C=\begin{bmatrix} c_{1}& -d_{1}& 0& 0&\dots 0& 0\\ 0& c_{2}& -d_{2}& 0&...

I have a bivariate modular polynomial of shape $$f(x,y)=x^2y-g(x)\equiv 0\bmod q$$ where $q=(2p-1)(2p+1)$ is a product of two primes $2p-1$ and $2p+1$, $g(x)\in\mathbb Z[x]$ is of degree four and $f(...

The Hurwitz integers are $$ \mathcal H= \{a+bi+cj+dk:a,b,c,d\in\mathbb Z\;\text{ or } \;a,b,c,d\in \tfrac12+\mathbb Z\}. $$ I want to know if there is a formula, for $m\in\mathbb Z$, for the number ...

$\DeclareMathOperator\Aut{Aut}\DeclareMathOperator\PSL{PSL}\DeclareMathOperator\GL{GL}\DeclareMathOperator\Aut{Aut}$Notation: $\GL(n, \mathbb{Z})$ to be the set of $n \times n$ invertible matrix, and ...