It is shown that the partial sums φn(s)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi _{n}(s)$$\end{document}, n>2\documentclass[12pt]{minimal}
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\begin{document}$$n>2$$\end{document}, of the series that defines the Fibonacci zeta function φ(s):=∑n=1∞Fn-s\documentclass[12pt]{minimal}
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\begin{document}$$\varphi (s):=\sum _{n=1}^{\infty }F_{n}^{-s}$$\end{document}, s∈C\documentclass[12pt]{minimal}
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\begin{document}$$s\in \mathbb {C} $$\end{document}, ℜs>0\documentclass[12pt]{minimal}
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\begin{document}$$\Re s>0$$\end{document} (Fn\documentclass[12pt]{minimal}
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\begin{document}$$F_{n}$$\end{document} 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 ρn\documentclass[12pt]{minimal}
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\begin{document}$$ \rho _{n}$$\end{document} corresponding to φn(s)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi _{n}(s)$$\end{document} coincide with an:=infℜs:φn(s)=0\documentclass[12pt]{minimal}
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\begin{document}$$a_{n}:=\inf \left\{ \Re s:\varphi _{n}(s)=0\right\} $$\end{document} for n>12\documentclass[12pt]{minimal}
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\begin{document}$$n>12$$\end{document}. As for the Henry upper bounds, we show that the limit limn→∞ρ0,n\documentclass[12pt]{minimal}
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\begin{document}$$\lim _{n\rightarrow \infty }\rho _{0,n}$$\end{document} exists and is the unique positive real number η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} such that φ(η)=4\documentclass[12pt]{minimal}
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\begin{document}$$\varphi (\eta )=4$$\end{document}. Its approximate value is 0,7570549496906548985355124…\documentclass[12pt]{minimal}
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\begin{document}$$0,7570549496906548985355124\ldots $$\end{document}. Finally, we prove that limn→∞an=-logϕ2\documentclass[12pt]{minimal}
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\begin{document}$$\lim _{n\rightarrow \infty }a_{n}=-\log _{\phi }2$$\end{document}, where ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document} is the golden ratio. As a consequence, all the zeros of all φn(s)\documentclass[12pt]{minimal}
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\begin{document}$$ \varphi _{n}(s)$$\end{document} lie essentially in the bounded vertical strip determined by the lines ℜs=\documentclass[12pt]{minimal}
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\begin{document}$$\Re s=$$\end{document}-logϕ2\documentclass[12pt]{minimal}
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\begin{document}$$-\log _{\phi }2$$\end{document} and ℜs=η\documentclass[12pt]{minimal}
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\begin{document}$$\Re s=\eta $$\end{document}.
