On the Order Estimates for Specific Functions of ζ(s) and its Contribution towards the Analytic Proof of The Prime Number Theorem

2023/08/28 by Subham De, De, Subham
Mathematics · #11A25 #11M06 #11M26 #11N37 Secondary 11-03 #30D30 #32E20 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Meromorphic and Entire Functions #Primary 11-02

paper · pdf · doi:10.48550/arxiv.2308.16303

openalex publication_date 2023/08/28 · openalex created_date 2023/09/03 · openalex updated_date 2026/07/28

Abstract

This article provides a proof of the famous Prime Number Theorem by establishing an analogous statement of the same in terms of the second Chebyshev Function ψ(x). We shall be extensively using complex analytic techniques in addition to certain meromorphic properties of the Reimann Zeta Function ζ(s) and its Analytic Continuation Property a priori using Riemann's Functional Equation in order to establish our desired result.

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