Introduction to the Theory of Algebraic Functions of One Variable - ISBN:0000000000

Introduction to the Theory of Algebraic Functions of One Variable

Date: 13 April 2011, 08:25

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An algebraic function у of a complex variable ? is a function which satisfies an equation of the form F(x, y) = 0, where F is a polynomial with complex coefficients; i.e., у is a root of an algebraic equation whose coefficients are rational functions of x. This very definition exhibits a strong similarity between the notions of algebraic function and algebraic number, the rational functions of ? playing a role similar to that played by the rational numbers. On the other hand, the equation F(x, y) = 0 may be construed to represent a curve in a plane in which ? and у are the coordinates, and this establishes an intimate link between
the theory of algebraic functions of one variable and algebraic geometry.

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