All Questions

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\PSL{PSL}$I want to ask the following, Given $X \in n \times n$ matrix that all the elements are integers and $X=X^{T}$ is symmetric. Can one always ...

Fix $n\geq 2$. Let $A$ be the matrix whose rows and columns are indexed by pairs $(a,b)\in \mathbb{Z}/n\mathbb{Z}$ such that $a,b$ generate $\mathbb{Z}/n\mathbb{Z}$ (the number of such pairs is $\phi(...

I'm trying to calculate an integral over the generalized Poincare upper half plane, then I find that I need to show the following identity: Let $X=(X_{i,j})\in\mathrm{GL}(n,\mathbb R)(n\geq 3)$ ...

I am interested in estimating how large determinants of matrices tend to be 'on average' given the following model: suppose we form $n \times n$ matrices $M$ such that all of the entries of $M$ are ...