1
The project
2
Basic definitions and notation
3
First approach: Wiener-Ikehara Tauberian theorem
▶
3.1
A Fourier-analytic proof of the Wiener-Ikehara theorem
3.2
Weak PNT
3.3
Removing the Chebyshev hypothesis
3.4
The prime number theorem in arithmetic progressions
3.5
The Chebotarev density theorem: the case of cyclotomic extensions
3.6
The Chebotarev density theorem: the case of abelian extensions
3.7
The Chebotarev density theorem: the general case
4
Second approach
▶
4.1
Residue calculus on rectangles
4.2
Perron Formula
4.3
Mellin transforms
4.4
Zeta Bounds
4.5
Proof of Medium PNT
4.6
MediumPNT
5
Third Approach
▶
5.1
Hadamard factorization
5.2
Hoffstein-Lockhart
5.3
Strong PNT
6
Elementary Corollaries
▶
6.1
Consequences of the PNT in arithmetic progressions
6.2
Consequences of the Chebotarev density theorem
7
Explicit estimates
▶
7.1
Mertens’ theorems
8
Tertiary explicit estimates
▶
8.1
Erdos problem 392
9
Iwaniec-Kowalski
▶
9.1
Blueprint for Iwaniec-Kowalski Chapter 1
10
Bombieri-Vinogradov
11
Bibliography
Dependency graph
Prime Number Theorem And ...
1
The project
2
Basic definitions and notation
3
First approach: Wiener-Ikehara Tauberian theorem
3.1
A Fourier-analytic proof of the Wiener-Ikehara theorem
3.2
Weak PNT
3.3
Removing the Chebyshev hypothesis
3.4
The prime number theorem in arithmetic progressions
3.5
The Chebotarev density theorem: the case of cyclotomic extensions
3.6
The Chebotarev density theorem: the case of abelian extensions
3.7
The Chebotarev density theorem: the general case
4
Second approach
4.1
Residue calculus on rectangles
4.2
Perron Formula
4.3
Mellin transforms
4.4
Zeta Bounds
4.5
Proof of Medium PNT
4.6
MediumPNT
5
Third Approach
5.1
Hadamard factorization
5.2
Hoffstein-Lockhart
5.3
Strong PNT
6
Elementary Corollaries
6.1
Consequences of the PNT in arithmetic progressions
6.2
Consequences of the Chebotarev density theorem
7
Explicit estimates
7.1
Mertens’ theorems
8
Tertiary explicit estimates
8.1
Erdos problem 392
9
Iwaniec-Kowalski
9.1
Blueprint for Iwaniec-Kowalski Chapter 1
10
Bombieri-Vinogradov
11
Bibliography