All Questions

On the basis of my computation, I have the following conjecture involving the secant function. Conjecture. Let $p$ be an odd prime and define $$S_p:=\det\left[\sec2\pi\frac{jk}p\right]_{0\le j,k\le (...

$\newcommand\Legendre{\genfrac(){}{}}$Let $p$ be an odd prime, and let $\Legendre\cdot p$ be the Legendre symbol. In 2003, Robin Chapman evaluated the determinants $$\det\left[\Legendre{i+j}p\right]_{...

Let $p$ be an odd prime. As in my paper, for $c,d\in\mathbb Z$ let us define $$[c,d]_p:=\det\left[\left(\frac{i^2+cij+dj^2}p\right)\right]_{0\le i,j\le p-1},$$ where $(\frac{\cdot}p)$ is the Legendre ...

Given an integer $n$, I want to prove the existence of an $n\times n$ binary matrix (with 0,1 entries), whose determinant is a prime number. What is a lower bound on the largest determinant that I ...

Let $p$ be an odd prime, and let $(\frac{\cdot}p)$ denote the Legendre symbol. Motivated by the evaluation of the determinants $$\det\left[\left(\frac{j+k}p\right)\right]_{1\le j,k\le(p-1)/2}\ \ \text{...