The Prime Counting Function

Sang-Un, Lee; MyeongBok Choi

Journal of The Korea Society of Computer and Information

Abbr : JKSCI
2011, 16(10), pp.101-110
Publisher : The Korean Society Of Computer And Information
Research Area : Computer Science

Sang-Un, Lee ¹, MyeongBok Choi ²

¹강릉원주대학교
²강릉원주대학교

ABSTRACT

The Riemann's zeta function has been known as answer for a number of primes less than given number . In prime number theorem, there are another approximation function , and . The error about is . The logarithmic integral function is . This paper shows that the can be represent with finite , and presents generalized prime counting function . Firstly, the can be represent to and such that . Then, is adjusted by with and error compensation value . As a results, this paper get the for . Then, this paper suggests a generalized function . The function superior than Riemann's zeta function in representation of prime counting.
KEYWORDS

prime number theorem, Riemann zeta function, natural logarithmic function, offset logarithmic integral function
REFERENCES (8)

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