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.