1
The project
2
First approach: Wiener-Ikehara Tauberian theorem.
▶
2.1
A Fourier-analytic proof of the Wiener-Ikehara theorem
2.2
Weak PNT
2.3
Removing the Chebyshev hypothesis
2.4
The prime number theorem in arithmetic progressions
2.5
The Chebotarev density theorem: the case of cyclotomic extensions
2.6
The Chebotarev density theorem: the case of abelian extensions
2.7
The Chebotarev density theorem: the general case
3
Second approach
▶
3.1
Residue calculus on rectangles
3.2
Perron Formula
3.3
Mellin transforms
3.4
Zeta Bounds
3.5
Proof of Medium PNT
3.6
MediumPNT
4
Third Approach
▶
4.1
Strong PNT
5
Elementary Corollaries
▶
5.1
Consequences of the PNT in arithmetic progressions
5.2
Consequences of the Chebotarev density theorem
6
Explicit estimates
7
Primary explicit estimates
▶
7.1
Definitions
7.2
The estimates of Fiori, Kadiri, and Swidinsky
7.3
Summary of results
8
Secondary explicit estimates
▶
8.1
Definitions
8.2
The arguments of Rosser and Schoenfeld
8.3
Summary of results
9
Tertiary explicit estimates
▶
9.1
The least common multiple sequence is not highly abundant for large \(n\)
Dependency graph
Prime Number Theorem And ...
1
The project
2
First approach: Wiener-Ikehara Tauberian theorem.
2.1
A Fourier-analytic proof of the Wiener-Ikehara theorem
2.2
Weak PNT
2.3
Removing the Chebyshev hypothesis
2.4
The prime number theorem in arithmetic progressions
2.5
The Chebotarev density theorem: the case of cyclotomic extensions
2.6
The Chebotarev density theorem: the case of abelian extensions
2.7
The Chebotarev density theorem: the general case
3
Second approach
3.1
Residue calculus on rectangles
3.2
Perron Formula
3.3
Mellin transforms
3.4
Zeta Bounds
3.5
Proof of Medium PNT
3.6
MediumPNT
4
Third Approach
4.1
Strong PNT
5
Elementary Corollaries
5.1
Consequences of the PNT in arithmetic progressions
5.2
Consequences of the Chebotarev density theorem
6
Explicit estimates
7
Primary explicit estimates
7.1
Definitions
7.2
The estimates of Fiori, Kadiri, and Swidinsky
7.3
Summary of results
8
Secondary explicit estimates
8.1
Definitions
8.2
The arguments of Rosser and Schoenfeld
8.3
Summary of results
9
Tertiary explicit estimates
9.1
The least common multiple sequence is not highly abundant for large \(n\)