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Montgomery, H.L, and Vaughan, R.C, Multiplicative number theory 1: Classical theory. vol.97, Cambridge university press, 2006.

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Article

Improved Estimate for the Prime Counting Function

1Department of Mathematics, African Institute for Mathematical Science, Ghana


Turkish Journal of Analysis and Number Theory. 2019, Vol. 7 No. 1, 1-4
DOI: 10.12691/tjant-7-1-1
Copyright © 2019 Science and Education Publishing

Cite this paper:
Theophilus Agama. Improved Estimate for the Prime Counting Function. Turkish Journal of Analysis and Number Theory. 2019; 7(1):1-4. doi: 10.12691/tjant-7-1-1.

Correspondence to: Theophilus  Agama, Department of Mathematics, African Institute for Mathematical Science, Ghana. Email: theophilus@aims.edu.gh, emperordagama@yahoo.com

Abstract

Using some simple combinatorial arguments, we establish some new estimates for the prime counting function and its allied functions. In particular we show that where This is an improvement to the estimate found in the literature.

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