2
$\begingroup$

A question on my last homework asks us to discuss the Riemann surface of $\sin(z)$. Since this isn't multivalued, the Riemann surface is trivial right?

Either I am missing something, which is entirely possible, or maybe this was a typo and he wanted us to discuss the Riemann surface of $\sin^{-1}(z).$

  • 0
    Ahlfors *Complex Analysis* (2nd ed. p.98) calls this the Riemann surface of the sin (or actually he does the cos), and describes it in some detail. Also, in a sense the Riemann surface of $w=f(z)$ is a graph of the parametrized relation $\{(w(t),z(t)) | w(t)=f(z(t))\}$ for all $t$, so it's a toss-up whether you call it the surface of the sin or of the $\sin^{-1}$.2016-08-18

0 Answers 0