Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.
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Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.
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In this book, Lang has set himself up the task of giving enough background material in order to study the theory of complex multiplication as given in Shimura-Taniyama's book: Complex multiplication of abelian varieties. This seems to preclude the successful try by A. Wiles to prove Fermat's Theorem through this path. The first edition is dated 1972 and the second came ten years later. This is now old theory but it still lies at graduate level nevertheless
