Dirichlet’s Theorem: Statement

attachments/Pasted%20image%2020220228153916.png

Strong Form and Proof

attachments/Pasted%20image%2020220228153933.png

Chebotarev Density

attachments/Pasted%20image%2020220228154024.png ## Splitting of Primes

attachments/Pasted%20image%2020220228154243.png

S&S

The Group of Units

attachments/Pasted%20image%2020220228154755.png

Infinitude of Primes

attachments/Pasted%20image%2020220228154818.png

Product Formula

attachments/Pasted%20image%2020220228155236.png

Proof of Dirichlet

attachments/Pasted%20image%2020220228155439.png

Counting Primes in 4k+1

attachments/Pasted%20image%2020220228155521.png

Computing an L function

attachments/Pasted%20image%2020220228155645.png

Proof

attachments/Pasted%20image%2020220228155703.png

Steps:

Prove a product formula
Make sense of taking log of both sides
Third:

Fourier Expansion

attachments/Pasted%20image%2020220228155811.png

Logs of L functions

attachments/Pasted%20image%2020220228161359.png

Fourier Series

Wave and Heat Equations

attachments/Pasted%20image%2020220228161854.png

attachments/Pasted%20image%2020220228162053.png

attachments/Pasted%20image%2020220228162144.png

Fourier Expansion

attachments/Pasted%20image%2020220228161953.png

attachments/Pasted%20image%2020220228162652.png

Links to this page

files without tags

Projects/2022 DRP/DRP Dirichlet Theorem on APs.md