On the zeros of the partial sums of the Fibonacci zeta function

It is shown that the partial sums ?(n)(s), n > 2, of the series that defines the Fibonacci zeta function ?(s) := (En=1Fn-s)-F-8 , s ? C, Rs> 0 (F(n )are the Fibonacci numbers), have infinitely many zeros in non-symmetrical vertical strips with respect to the imaginary axis. Using two theorems of Carmichael and Bohr, we prove that the Henry lower bounds ?(n) corresponding to ?(n)(s) coincide with a(n) := inf {Rs : ?(n) (s) = 0} for n > 12. As for the Henry upper bounds, we show that the limit lim(n?8) ?0,(n) exists and is the unique positive real number ? such that ?(?) = 4. Its approximate value is 0, 7570549496906548985355124.... Finally, we prove that lim(n?8) a(n) = - log(f) 2, where f is the golden ratio. As a consequence, all the zeros of all ?n (s) lie essentially in the bounded vertical strip determined by the lines Rs = - log(f )2 and Rs = ?.