论文标题
Riemann XI功能的Jensen多项式和渐近学的零
Zeros of Jensen polynomials and asymptotics for the Riemann xi function
论文作者
论文摘要
詹森（Riemann）假设的詹森（Jensen）的经典标准是所有相关的詹森多项式仅具有真实的零。我们使用Hermite多项式的线性组合找到了该标准的新版本，并表明这种情况在许多情况下都存在。详细的渐近扩展是针对XI功能所需的Taylor系数（$ 1/2 $）以及相关数量的。这些结果是基于最近的格里芬，ono，rolen和Zagier的结果。
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 combinations of Hermite polynomials, and show that this condition holds in many cases. Detailed asymptotic expansions are given for the required Taylor coefficients of the xi function at $1/2$ as well as related quantities. These results build on those in the recent paper of Griffin, Ono, Rolen and Zagier.
