Beurling integers with RH and large oscillation
Advances in Mathematics(2020)
摘要
We construct a Beurling generalized number system satisfying the Riemann hypothesis and whose integer counting function displays extremal oscillation in the following sense. The prime counting function of this number system satisfies π(x)=Li(x)+O(x), while its integer counting function satisfies the oscillation estimate N(x)=ρx+Ω±(xexp(−clogxloglogx)) for some c>0, where ρ>0 is its asymptotic density. The construction is inspired by a classical example of H. Bohr for optimality of the convexity bound for Dirichlet series, and combines saddle-point analysis with the Diamond-Montgomery-Vorhauer probabilistic method via random prime number system approximations.
更多查看译文
关键词
primary,secondary
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要