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Let us consider the Riemann Zeta function non-trivial zeros $\rho_{n}=\frac{1}{2} + i\gamma_{n}$.

Let us now consider the following sum: $\tau (n)=\sum_{k=1}^{n}\sin(k)\sin(\gamma _{k})$

where:

$\gamma _{1}=14.1347251417346...$

$\gamma _{2}=21.0220396387715...$

$\gamma _{3}=25.0108575801456...$

etc

This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$:

My question is: does anyone know any articles where this periodicity is investigated? 

Let us consider the Riemann Zeta function non-trivial zeros $\rho_{n}=\frac{1}{2} + i\gamma_{n}$.

Let us now consider the following sum: $\tau (n)=\sum_{k=1}^{n}\sin(k)\sin(\gamma _{k})$

where:

$\gamma _{1}=14.1347251417346\ldots$

$\gamma _{2}=21.0220396387715\ldots$

$\gamma _{3}=25.0108575801456\ldots$

etc

This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$:

My question is: does anyone know any articles where this periodicity is investigated? 

Let us consider the imaginary parts of the Riemann Zeta function non-trivial zeros $\rho _{n}$.

Let us now consider the following sum: $\tau (n)=\sum_{1}^{n}\sin(n)\sin(\rho _{n})$

This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$:

My question is: does anyone know any articles where this periodicity is investigated? 

Let us consider the Riemann Zeta function non-trivial zeros $\rho_{n}=\frac{1}{2} + i\gamma_{n}$.

Let us now consider the following sum: $\tau (n)=\sum_{k=1}^{n}\sin(k)\sin(\gamma _{k})$

where:

$\gamma _{1}=14.1347251417346...$

$\gamma _{2}=21.0220396387715...$

$\gamma _{3}=25.0108575801456...$

etc

This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$:

My question is: does anyone know any articles where this periodicity is investigated? 

Let us consider the imaginary parts of the Riemann Zeta function non-trivial zeros $\rho _{n}$.

Let us now consider the following sum: $\tau (n)=\sum_{1}^{n}\sin(n)\sin(\rho _{n})$

This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$: Plot 1

My question is: does anyone know any articles where this periodicity is investigated?

Let us consider the imaginary parts of the Riemann Zeta function non-trivial zeros $\rho _{n}$.

Let us now consider the following sum: $\tau (n)=\sum_{1}^{n}\sin(n)\sin(\rho _{n})$

This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$:

My question is: does anyone know any articles where this periodicity is investigated?