In Section 4 of the Introduction it became clear that the state of analysis in the first half of the 19th century hardly justified referring to it as systematically ordered. In particular, this was true of complex analysis, whose evolution up to Riemann’s time we are about to describe. If our account is to be reasonably systematic, then we cannot fully adhere to the chronological development: some things that came into being prior to the firm establishment of the complex numbers were tacked on to complex function theory much later, and impressive results involving complex integration were obtained before the need arose for a justification of complex differentiation. The historical evolution of complex analysis was different from the genetic construction we feel tempted to make up today.
KeywordsRiemann Surface Complex Analysis Zeta Function Algebraic Function Monogenic Function
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