Gasper's determinant theorem, revisited

Abstract

Let $n\ge 2$ be a natural number, $M$ a real $n\times n$ matrix, $s$ the sum of the entries of $M$ and $q$ the sum of their squares. With $\alpha :=s/n$ and $\beta :=q/n$, Gasper's determinant bound says that $|\det M|\le {\beta }^{n/2}$, and in case of ${\alpha }^2\ge \beta$: $$|\det M|\le |\alpha |{\left(\frac{n\beta -{\alpha }^2}{n-1}\right)}^{\frac{n-1}{2}}$$ This article gives a corrected proof of Gasper's theorem and lists some more applications.