The Riemann hypothesis is true up to 3·1012 - Platt - 2021 - Bulletin of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …

Many papers have studied inequalities for partition functions. Recently, a number of papers
have considered mixtures between additive and multiplicative behavior in such inequalities …

We define a new class of functions, connected to the classical Laguerre–Pólya class, which
we call the shifted Laguerre–Pólya class. Recent work of Griffin, Ono, Rolen, and Zagier …

The Turán inequality, the Laguerre inequality and their m-rd generalizations have been
proved to be closely relative with the Laguerre-Pólya class and Riemann hypothesis. Since …

In this paper, we give an iterated approach to concern with the positivity of\begin
{equation*}\det\(p (n-i+ j)) _ {1\leq i, j\leq k},\end {equation*} where $ p (n) $ is the partition …

The classical criterion of Jensen for the Riemann hypothesis is that all of the associated
Jensen polynomials have only real zeros. We find a new version of this criterion, using linear …

Abstract In 2007, Andrews and Paule introduced the broken k-diamond partition function Δ k
(n), whose arithmetic properties have received considerable attention. In this paper, we will …

In this paper, we find some conditions under which a sequence $\{\alpha (n)\} $ will satisfy
the Laguerre inequality of any order asymptotically. Using this method, we prove that for any …

Abstract The Boros-Moll numbers di (m) arise from a quartic integral studied by Boros and
Moll. For fixed m, the sequence {di (m)} 0≤ i≤ m has been proven to satisfy the Turán …

Motivated by a recent pseudo-spin model for monolayer-bilayer phase transitions in silver-
based honeycomb layered materials, we propose that the critical pseudo-magnetic fields in …