Applying a theorem of Reich on Dirichlet series satisfying difference-differential equations, we show that the Fibonacci zeta-function satisfies no algebraic differential equation.
@article{1505, title = {The Fibonacci Zeta-Function is Hypertranscendental}, journal = {CUBO, A Mathematical Journal}, volume = {10}, year = {2008}, language = {en}, url = {http://dml.mathdoc.fr/item/1505} }
Steuding, J¨orn. The Fibonacci Zeta-Function is Hypertranscendental. CUBO, A Mathematical Journal, Tome 10 (2008) . http://gdmltest.u-ga.fr/item/1505/