# Gaussian Primes

![](attachments/Pasted%20image%2020220211131539.png)
![](attachments/Pasted%20image%2020220211131509.png)
![](attachments/Pasted%20image%2020220211131523.png)
Better:
$$
L_{r_2}(s      , \chi) = \sum_{0\leq n\leq r^2} {r_2(n) \chi(n) \over n^s}, \qquad \chi(n) = 1 \, \forall n
$$
![](attachments/Pasted%20image%2020220211131622.png)
![](attachments/Pasted%20image%2020220211131638.png)


## Sum of Squares
![](attachments/Pasted%20image%2020220211131715.png)
![](attachments/Pasted%20image%2020220211131741.png)
![](attachments/Pasted%20image%2020220211131858.png)
## Results
![](attachments/Pasted%20image%2020220211125806.png)
![](attachments/Pasted%20image%2020220211125818.png)
![](attachments/Pasted%20image%2020220211130724.png)
# Examples

![](attachments/Pasted%20image%2020220211130505.png)
![](attachments/Pasted%20image%2020220211130530.png)