黎曼zeta函数在短区间内的简单临界零点和互异零点
Simple critical zeros and distinct zeros of the Riemann zeta function in short intervals
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中文总结 AI 辅助
本文利用Lamzouri的方法，结合Montgomery对关联定理的短区间版本，给出黎曼zeta函数在短区间内非平凡零点数量的下界。
中文摘要 AI 辅助
最近，关于黎曼zeta函数的非平凡零点，Claude发现并由Alpöge和Furman验证，超过67.25%的零点在临界线上且是简单的，超过83.62%的零点是互异的。后来，Lamzouri给出了一种不同且更直接的证明。在本文中，我们将使用Lamzouri的方法给出黎曼zeta函数在短区间内非平凡零点数量的下界。为了证明主要结果，我们遵循Baluyot、Goldston、Suriajaya和Turnage-Butterbaugh的方法，建立了Montgomery关于zeta函数零点在短区间内对关联的定理，然后使用Lamzouri关于任何在复共轭下不变的有限复数多重集的不等式。
英文摘要
Recently, on the non-trivial zeros of the Riemann zeta function, it is obtained by Alpöge and Furman that more than 67.25% of the zeros are simple and on the critical line, and more than 83.62% are distinct. Later, Lamzouri gave a different and more direct proof. In this article, we will use the method of Lamzouri to give lower bounds on the number of the non-trivial zeros of the Riemann zeta function in short intervals. To prove the main result, we establish Montgomery's theorem on the pair correlation of zeros of the zeta function in short intervals by following the approach of Baluyot, Goldston, Suriajaya and Turnage-Butterbaugh, and then use Lamzouri's inequality on any finite multiset of complex numbers which is invariant under complex conjugation.
发表机构
- Yunnan University（云南大学）
机构由 AI 辅助整理，请以论文原文为准。
