Gaussian Primes

![[attachments/Pasted%20image%2020220211131539.png) attachments/Pasted%20image%2020220211131509.png ![](attachments/Pasted%20image%2020220211131523.png]] Better: \begin{align*} 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 \end{align*} ![[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]]

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