[Riemann zeta function](https://en.wikipedia.org/wiki/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 $1$.



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> > **My question here is:**
> >  Could the Riemann zeta function be a solution for a known differential equation?
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**Note:** I would like if there is a paper or ref show that zeta function presented a solution for known Differential equation.



Could the Riemann zeta function be a solution for a known differential equation?
When posed properly, a long-standing open problem, but in the form you ask:


*Robert A. Van Gorder*, MR 3276353 [**Does the Riemann zeta function satisfy a differential equation?**](http://dx.doi.org/10.1016/j.jnt.2014.08.013), *J. Number Theory* **147** (2015), 778--788.


