Introduction to Algebraic and Abelian Functions

1. Front Matter

   Pages i-ix

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2. The Riemann-Roch Theorem

   • Serge Lang

   Pages 1-35

3. The Fermat Curve

   • Serge Lang

   Pages 36-45

4. The Riemann Surface

   • Serge Lang

   Pages 46-53

5. The Theorem of Abel-Jacobi

   • Serge Lang

   Pages 54-71

6. Periods on the Fermat Curve

   • Serge Lang

   Pages 72-81

7. Linear Theory of Theta Functions

   • Serge Lang

   Pages 83-109

8. Homomorphisms and Duality

   • Serge Lang

   Pages 110-130

9. Riemann Matrices and Classical Theta Functions

   • Serge Lang

   Pages 131-142

10. Involutions and Abelian Manifolds of Quaternion Type

    • Serge Lang

    Pages 143-155

11. Theta Functions and Divisors

    • Serge Lang

    Pages 156-164

12. Back Matter

    Pages 165-169

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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.

• Abelsche Funktion
• Algebraic
• Algebraische Funktion
• Functions
• Lattice
• logarithm

Second Edition

S. Lang

Introduction to Algebraic and Abelian Functions

"An excellent and very readable introduction to basic notions in algebraic geometry."—MATHEMATICAL REVIEWS

• Department of Mathematics, Yale University, New Haven, USA

  Serge Lang

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