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- W3004177140 abstract "Part One: The main work in this paper is on properties of the logarithmic integral $Li(x)$ and the prime counting function $pi(x)$. Let define the truncation of the logarithmic integral $Li(x)$ as [pi^{*}(x,N):=frac{x}{log x}sum_{n=0}^{N}frac{n!}{log^{n}x}.] Firstly, we prove $Li(x)-pi^{*}(x,M) 0$, and $xgeq x_{beta}$ which satisfies $(log x_{beta})^{2}/x_{beta}^{0.0327283}leqbeta$. Then there are [ frac{pi(x+Phi(x))-pi(x)}{Phi(x)/log x}=1+O(frac{1}{log x}) ] and [ lim_{x to infty}frac{pi(x+Phi(x))-pi(x)}{Phi(x)/log x}=1. ]" @default.
- W3004177140 created "2020-02-07" @default.
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- W3004177140 date "2011-10-12" @default.
- W3004177140 modified "2023-09-27" @default.
- W3004177140 title "On more accurate estimation of prime numbers, and primes in short intervals, and distribution of nontrivial zeros of the Riemann zeta function" @default.
- W3004177140 hasPublicationYear "2011" @default.
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