论文标题
Riemann Zeta功能的零之间的差距上的一些明确和无条件的结果
Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function
论文作者
论文摘要
我们将heath棕褐色的论点显式，涉及riemann zeta功能的非平凡零之间的大小差距，$ζ（s）$。特别是，我们在差距（大小）上提供了第一个无条件结果，该结果符合零比例的正。为此，我们证明了$ s（t+h）-s（t）$的第二和第四功率矩的明确界限，其中$ s（t）$表示关键行上的$ζ（s）$的参数和$ h \ ll 1 / \ log log t $。我们还使用这些力矩来证明给定多重性的$ζ（s）$的非平凡零的密度。
We make explicit an argument of Heath-Brown concerning large and small gaps between nontrivial zeroes of the Riemann zeta-function, $ζ(s)$. In particular, we provide the first unconditional results on gaps (large and small) which hold for a positive proportion of zeroes. To do this we prove explicit bounds on the second and fourth power moments of $S(t+h)-S(t)$, where $S(t)$ denotes the argument of $ζ(s)$ on the critical line and $h \ll 1 / \log T$. We also use these moments to prove explicit results on the density of the nontrivial zeroes of $ζ(s)$ of a given multiplicity.
