International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Call for Papers | Fully Refereed | Open Access | Double Blind Peer Reviewed

ISSN: 2319-7064


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Review Papers | Mathematics | India | Volume 12 Issue 11, November 2023


On the proof of the Prime Number Theorem using Order Estimates for the Chebyshev Theta Function

Subham De [2]


Abstract: In this paper, we shall study the stellar work of Norwegian mathematician Selberg and Hungarian mathematician Erd"os in providing an Elementary proof of the well-known Prime Number Theorem. In addition to introducing ourselves to the notion of Arithmetic Functions, we shall primarily focus our research on obtaining suitable estimates for the Chebyshev Theta Function v(x). Furthermore, we'll try to infer about the asymptotic properties of another function p(x), which shall be needed later on in establishing an equivalent statement of our main result. All the mathematical terminologies pertinent to the proof have been discussed in the earlier sections of the text.


Keywords: Prime Number Theorem, Arithmetic Functions, Partial Summation Formula, Primes, Riemann Zeta Function


Edition: Volume 12 Issue 11, November 2023,


Pages: 1677 - 1691


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