Editing Thue–Morse sequence (section)

===Riemann zeta function===
Certain linear combinations of Dirichlet series whose coefficients are terms of the Thue–Morse sequence give rise to identities involving the Riemann Zeta function (Tóth, 2022 <ref>
{{cite journal|author1-link=Tóth|last1=Tóth|first1=László|title=Linear Combinations of Dirichlet Series Associated with the Thue-Morse Sequence|journal=Integers|volume=22|year=2022|issue=article 98|arxiv=2211.13570 }}
</ref>). For instance:
:<math>  \begin{align}
    \sum_{n\geq1} \frac{5 t_{n-1} + 3 t_n}{n^2} &= 4 \zeta(2) = \frac{2 \pi^2}{3}, \\
	\sum_{n\geq1} \frac{9 t_{n-1} + 7 t_n}{n^3} &= 8 \zeta(3),\end{align}</math>
where <math>(t_n)_{n\geq0}</math> is the <math>n^{\rm th}</math> term of the Thue–Morse sequence. In fact, for all <math>s</math> with real part greater than <math>1</math>, we have
:<math>  (2^s+1) \sum_{n\geq1} \frac{t_{n-1}}{n^s} + (2^s-1) \sum_{n\geq1} \frac{t_{n}}{n^s} = 2^s \zeta(s).</math>