If $m$ divides $n$ then $\sin(n\pi/m) = 0$. By counting number of zeros of $\sin(n\pi/m)$ for a given $n \in \mathds{Z}$ and $m \in \mathds{Z}$, we can find the total number of divisors that $n$ has and in this way, we can construct a series representation of the \emph{Number-of-divisors function}, $\mathcal{S}(n)$. Similarly, we can find a closed-form of another important integer-valued function in Number Theory, \emph{Sum-of-divisors function}, $\sigma(n)$. After constructing series representation of these functions we can resolve a well-known conjecture in Number Theory -- the \emph{Riemann Conjecture}. To conclude the Riemann conjecture we use \emph{Robin's inequality} which sets an upper limit of $\sigma(n)$ for $n>5040$, if Riemann conjecture is true. This method can be trivially extended to the other higher-order divisor functions. To construct these series representations we have explored \emph{Matsubara} technique which is commonly used in Condensed Matter Physics to perform various sums over integer index with a contour integral.