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

A consideration of the investigations in the first part of Riemann'sTheory of Abelian Functions, this volume introduces Riemann's approach to multiple-value functions and the geometrical representation of these functions by what later became known as Riemann surfaces. It further concentrates on the kinds of functions that can be defined on these surfaces, confining the treatment to rational functions and their integrals, and then demonstrates how Riemann's mathematical ideas about Abelian integrals can be arrived at by thinking in terms of the flow of electric current on surfaces. Deeply significant in the area of complex functions, this work constitutes one of the best introductions to the origins of topological problems. Unabridged republication of the classic 1893 edition. 43 figures. Glossary.Klein, Félix is the author of 'On Riemann's Theory of Algebraic Functions and Their Integrals A Supplement to the Usual Treatises' with ISBN 9780486495521 and ISBN 0486495523.