Sharp inequalities for symmetric polynomials, Hunter's conjecture, and moments of exponential random variables

Silouanos Brazitikos, Christos Pandis

We prove Hunter's conjecture on complete homogeneous symmetric polynomials. For even $n$ and every integer $k\ge 1$, we show that under the constraint ${\sum }_{i=1}^n{a}_i^2=1$ the g…