素数的理性与非理性计数
Counting Primes Rationally And Irrationally
摘要：
最近的技术估计下界的素数计数函数$π(x)=#\{p \leq x: p\text{ prime}\}$的非理性措施$μ(ζ(s)) \geq 2$的zeta函数的特殊值的装置声称，$π(x) \gg \log \log x/\log \log \log x$。本文将下界改进为$π(x) \gg \log x$，并将分析推广到zeta函数有理比的无理性测度$μ(ζ(s)) \geq 1$.
英文摘要：
The recent technique for estimating lower bounds of the prime counting function $π(x)=#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures $μ(ζ(s)) \geq 2$ of special values of the zeta function claims that $π(x) \gg \log \log x/\log \log \log x$. This note improves the lower bound to $π(x) \gg \log x$, and extends the analysis to the irrationality measures $μ(ζ(s)) \geq 1$ for rational ratios of zeta functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
