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The Riemann surfaces of a function and its fractional integral

Published online by Cambridge University Press:  31 October 2008

William Fabian
William Fabian
Affiliation:
14 Grosvenor Avenue, Canonbury, London, N.5.
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1. Introduction. For a many-valued function f(z) of the complex variable z, a Riemann surface can be constructed such that, at any point z on the surface, the function has only one value; a function normally multiform, is therefore uniform on a certain Riemann surface.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 39 , January 1954 , pp. 14 - 16
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

1 Fabian, , Phil. Mag., 39, 783 (1935).Google Scholar

1 Fabian, : Phil. Mag., 39, 277 (1936).Google Scholar

2 If f(z) has M cycles at p, f(z) is to be regarded as having M branch-points at p, and the theorem applies to each of these branch-points separately.

1 Fabian, : Phil. Mag., 39, 276 (1936).Google Scholar