Functions of a Complex Variable
by Thomas Murray MacRobert
Publisher: The Macmillan Company 1917
Number of pages: 328
This book is designed for students who, having acquired a good working knowledge of the calculus, desire to become acquainted with the theory of functions of a complex variable, and with the principal applications of that theory. In order to avoid making the subject too difficult for beginners, I have abstained from the use of strictly arithmetical methods, and have, while endeavouring to make the proofs sufficiently rigorous, based them mainly on geometrical conceptions.
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by Curtis McMullen - Harvard University
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
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A systematic study of Riemann matrices which arise in a natural way from the theory of abelian functions. Contents: Abelian Functions; Commutator-algebra of a R-matrix; Division algebras over Q with a positive involution; Cyclic algebras; etc.
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