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
3.7
Strong PNT
4
Elementary Corollaries
▶
4.1
Consequences of the PNT in arithmetic progressions
4.2
Consequences of the Chebotarev density theorem
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
3.7
Strong PNT
4
Elementary Corollaries
4.1
Consequences of the PNT in arithmetic progressions
4.2
Consequences of the Chebotarev density theorem