A new theorem on the prime-counting function
نویسندگان
چکیده
منابع مشابه
On the Means of the Values of Prime Counting Function
In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.
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The paper describes a systematic computational study of the prime counting function π(x) and three of its analytic approximations: the logarithmic integral li(x) := ∫ x 0 dt log t , li(x)− 2 li( √ x), and R(x) := ∞k=1 μ(k)li(x1/k)/k, where μ is the Möbius function. The results show that π(x) < li(x) for 2 ≤ x ≤ 1014, and also seem to support several conjectures on the maximal and average errors...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2015
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-015-9702-z