On linear relations for Dirichlet series formed by recursive sequences of second order

Carsten Elsner, Niclas Technau

Let $F_n$ and $L_n$ be the Fibonacci and Lucas numbers, respectively. Four corresponding zeta functions in $s$ are defined by \[ζ_F(s) \,:=\, \sum_{n=1}^{\infty} \frac{1}{F_n^s}\,,…