the derivation of the this result). The Euler-Riemann zeta function is denoted $\zeta(s)$. Hence the modulation requires spin-orbit coupling and a tilted Zeeman field, with $h_x$ and $h_z$ both finite, and $q_0 \propto h^3\,\alpha^3$, which is in contrast with the 2D case, where $q_0 \propto h\,\alpha^3$ [@konschelle_theory_2015; @edelstein_magnetoelectric_1995].

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We conclude this section by a discussion of the observability of the modulated state in wires with weak SO coupling. In order to evaluate the order of magnitude of $q_0$, we replace the mass $m$ in Eq. (\[q0\_weak\]) by its expression in terms of $\mu$ and $k_F$ for an ideal parabolic band. We obtain : $$q_0  \simeq  \frac{127}{32\,\pi^4} \frac{\zeta(7)}{\zeta(3)}  \, \, \frac{h_x^2\,h_z\,\tilde{\alpha}^3}{\,T_c^4 \mu^2}  k_F^4 \, \,\;,
    \label{q0_weak_eval}$$ where the $\hbar$ factors disappears. The spin-orbit coupling has been expressed by the parameter $ \tilde{\alpha}$ : $$\tilde{\alpha}= \hbar \alpha  \,\;,
    \label{alphatilde}$$ which is commonly used in experimental works on spin-orbit systems. The modulation is very sensitive to the value of this spin-orbit coupling. In the regime of weak SO coupling corresponding to the range $ \tilde{\alpha}= 1-10 \, \,  {\rm meV}.{\text{\normalfont\AA}}$, the modulation wavevector $q_0$ reaches extremely small values (in comparison to $k_F \simeq 0.6$ A$^{-1}$) which justifies [*a posteriori*]{} the expansion in 