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.
Best Answer
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?, J. Number Theory 147 (2015), 778--788.