Riemann zeta function is a function of complex variable $s$ that analytically continous the sum of Dirichlet series .defined as :$$\zeta(s)=\sum_{n=1}^{\infty}\displaystyle \frac{1}{n^s} $$ for when the real part is greater than $1$.

My question here is:Could the Riemann zeta function be a solution for a known differential equation?

**Note:** I would like if there is a paper or ref show that zeta function presented a solution for known Differential equation.

autonomousdifferential equation (one which does not explicitly involve $s$). $\endgroup$ – Terry Tao Jan 21 '17 at 23:06