Author

Yan-Xin Liu

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Preprint Sep 2026

Preservation of log-concavity under Hadamard products

For a nonzero real polynomial $p$, let $\W(p)$ denote the numerator of its ordinary generating function. We prove that if the coefficients of both $\W(p)$ and $\W(q)$ are nonnegative and log-concave with no internal zeros, then so are the coefficients of $\W(pq)$. This provides an affirmative answer to a question of Br...

Yan-Xin Liu, Jian-Xi Mao · 0 citations

Preprint Oct 2026

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...

Yan-Xin Liu, Jian-Xi Mao · 1 citation · ⚡1