@article{ART001597352},
author={Sang-Un, Lee and MyeongBok Choi},
title={The Prime Counting Function},
journal={Journal of The Korea Society of Computer and Information},
issn={1598-849X},
year={2011},
volume={16},
number={10},
pages={101-110}
TY - JOUR
AU - Sang-Un, Lee
AU - MyeongBok Choi
TI - The Prime Counting Function
JO - Journal of The Korea Society of Computer and Information
PY - 2011
VL - 16
IS - 10
PB - The Korean Society Of Computer And Information
SP - 101
EP - 110
SN - 1598-849X
AB - 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.
KW - prime number theorem;Riemann zeta function;natural logarithmic function;offset logarithmic integral function
DO -
UR -
ER -
Sang-Un, Lee and MyeongBok Choi. (2011). The Prime Counting Function. Journal of The Korea Society of Computer and Information, 16(10), 101-110.
Sang-Un, Lee and MyeongBok Choi. 2011, "The Prime Counting Function", Journal of The Korea Society of Computer and Information, vol.16, no.10 pp.101-110.
Sang-Un, Lee, MyeongBok Choi "The Prime Counting Function" Journal of The Korea Society of Computer and Information 16.10 pp.101-110 (2011) : 101.
Sang-Un, Lee, MyeongBok Choi. The Prime Counting Function. 2011; 16(10), 101-110.
Sang-Un, Lee and MyeongBok Choi. "The Prime Counting Function" Journal of The Korea Society of Computer and Information 16, no.10 (2011) : 101-110.
Sang-Un, Lee; MyeongBok Choi. The Prime Counting Function. Journal of The Korea Society of Computer and Information, 16(10), 101-110.
Sang-Un, Lee; MyeongBok Choi. The Prime Counting Function. Journal of The Korea Society of Computer and Information. 2011; 16(10) 101-110.
Sang-Un, Lee, MyeongBok Choi. The Prime Counting Function. 2011; 16(10), 101-110.
Sang-Un, Lee and MyeongBok Choi. "The Prime Counting Function" Journal of The Korea Society of Computer and Information 16, no.10 (2011) : 101-110.
