Yan-Xin Liu

Infinite log-concavity of the Taylor coefficients of the Riemann xi-function

The Riemann hypothesis is equivalent to $F(x)$ belonging to the Laguerre--P\'olya class. Br\"and\'en [J. Reine Angew. Math., 2011] proved that if an entire function in the Laguerre--P\'olya class has nonnegative Taylor coefficients, then its coefficient sequence is infinitely log-concave. Consequently, the Riemann hypo...