A degree-linear upper bound for the Pólya exponent of forms with fixed arity

Yulong Li, Colin Tan

Let $P={\sum }_{\omega }{a}_{\omega }{x}^{\omega }$ be a degree $d$ homogeneous polynomial in $x_0,\dots ,x_n$ with real coefficients. Pólya showed that, if $P$ is strictly positive on the standard $n$-simpl…