Question

Suppose it is known that the point $z_0=+38$ (or $z_0=-38$, or $\left.z_0= \pm 16\right)$ is a branch point of the function $w(z)$ expressing the roots of equation (2.8) in terms of the parameter $z$. How do the sheets of the Riemann surface of the function $w(z)$ at the point $z_0$ (more precisely, along the cuts joining the point $z_0$ to infinity; cf., Remark $$2, \$ 2.10$$ ) join?

    Suppose it is known that the point $z_0=+38$ (or $z_0=-38$, or $\left.z_0= \pm 16\right)$ is a branch point of the function $w(z)$ expressing the roots of equation (2.8) in terms of the parameter $z$. How do the sheets of the Riemann surface of the function $w(z)$ at the point $z_0$ (more precisely, along the cuts joining the point $z_0$ to infinity; cf., Remark $$2, \$ 2.10$$ ) join?
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Abel'S Theorem in Problems and Solutions Based on the Lectures of Professor V.I. Arnold
Abel'S Theorem in Problems and Solutions Based on the Lectures of Professor V.I. Arnold
V.B. Alekseev,… 1st Edition
Chapter 2, Problem 346 ↓

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A branch point is a point where the function \( w(z) \) is not single-valued. In this case, \( z_0 = +38 \), \( z_0 = -38 \), or \( z_0 = \pm 16 \) are given as branch points. This means that as we encircle these points in the complex plane, the value of \( w(z)  Show more…

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Suppose it is known that the point $z_0=+38$ (or $z_0=-38$, or $\left.z_0= \pm 16\right)$ is a branch point of the function $w(z)$ expressing the roots of equation (2.8) in terms of the parameter $z$. How do the sheets of the Riemann surface of the function $w(z)$ at the point $z_0$ (more precisely, along the cuts joining the point $z_0$ to infinity; cf., Remark $$2, \$ 2.10$$ ) join?
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