J. Holland

A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's $\xi$-function

Let \[ \xi\!\left(\frac12+z\right) =\sum_{n\geq 0}\frac{\gamma(n)}{n!}z^{2n}, \qquad J^{d,n}(X) =\sum_{j=0}^{d}\binom dj\gamma(n+j)X^j . \] The Riemann hypothesis is equivalent to the hyperbolicity of $J^{d,n}$ for every $d,n\geq0$. We prove that there is an absolute constant $K>0$ such that \[ n^3\log^2(n+2)\geq Kd^5...