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/