In complex analysis, how are multivalued functions represented using riemann surfaces.?

Answer 1

Riemann surfaces are associated with a function of a complex variable by means of a holomorphic function (see wiki). Multivalued functions of a complex variable are frequently represented by sheeted Riemann surfaces, which are much like parking structures where one winds up or down floors. Check the link to Planet Math's article on this, see "Riemann's Construction" in particular (see link). You should keep in mind that Riemann surfaces are often analytic continuations of functions of complex variables, so that they can have "more information". They are devices to aid understanding functions of a complex variable that really need 4 dimensions to be able to visualize entirely.