On the Order Estimates for Specific Functions of $ζ(s)$ and its Contribution towards the Analytic Proof of The Prime Number Theorem
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917060183851008 |
|---|---|
| author | De, Subham |
| author_facet | De, Subham |
| contents | This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $ψ(x)$. We shall be extensively using complex analytic techniques in addition to certain meromorphic properties of the \textit{Reimann Zeta Function} $ζ(s)$ and its \textit{Analytic Continuation Property} a priori using Riemann's Functional Equation in order to establish our desired result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16303 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Order Estimates for Specific Functions of $ζ(s)$ and its Contribution towards the Analytic Proof of The Prime Number Theorem De, Subham General Mathematics Primary 11-02, 11A25, 11M26, 11N37 Secondary 11-03, 11M06, 30D30, 32E20 This article provides a proof of the famous \textit{Prime Number Theorem} by establishing an analogous statement of the same in terms of the second \textit{Chebyshev Function} $ψ(x)$. We shall be extensively using complex analytic techniques in addition to certain meromorphic properties of the \textit{Reimann Zeta Function} $ζ(s)$ and its \textit{Analytic Continuation Property} a priori using Riemann's Functional Equation in order to establish our desired result. |
| title | On the Order Estimates for Specific Functions of $ζ(s)$ and its Contribution towards the Analytic Proof of The Prime Number Theorem |
| topic | General Mathematics Primary 11-02, 11A25, 11M26, 11N37 Secondary 11-03, 11M06, 30D30, 32E20 |
| url | https://arxiv.org/abs/2308.16303 |