Excerpt from On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises

Theory of Functions treated geometrically. Part I, Winter-semester 1880 81, Part II, Summer-semester 1881.

I denote thus the contents of the investigations with which Riemann was concerned in the first part of his Theory of the Abelian Functions. The theory of the O-functions, as developed in the second part of the same treatise, is in the first place, as we know, of an essentially different character, and is excluded from the following presentation as it was from my course of lectures.

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