Author | Lang, Serge. author |
---|---|
Title | Introduction to Algebraic and Abelian Functions [electronic resource] / by Serge Lang |
Imprint | New York, NY : Springer New York, 1982 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5740-0 |
Descript | X, 170 p. online resource |
I The Riemann-Roch Theorem -- ยง1. Lemmas on Valuations -- ยง2. The Riemann-Roch Theorem -- ยง3. Remarks on Differential Forms -- ยง4. Residues in Power Series Fields -- ยง5. The Sum of the Residues -- ยง6. The Genus Formula of Hurwitz -- ยง7. Examples -- ยง8. Differentials of Second Kind -- ยง9. Function Fields and Curves -- ยง10. Divisor Classes -- II The Fermat Curve -- ยง1. The Genus -- ยง2. Differentials -- ยง3. Rational Images of the Fermat Curve -- ยง4. Decomposition of the Divisor Classes -- III The Riemann Surface -- ยง1. Topology and Analytic Structure -- ยง2. Integration on the Riemann Surface -- IV The Theorem of Abel-Jacobi -- ยง1. Abelian Integrals -- ยง2. Abelโs Theorem -- ยง3. Jacobiโs Theorem -- ยง4. Riemannโs Relations -- ยง5. Duality -- V Periods on the Fermat Curve -- ยง1. The Logarithm Symbol -- ยง2. Periods on the Universal Covering Space -- ยง3. Periods on the Fermat Curve -- ยง4. Periods on the Related Curves -- VI Linear Theory of Theta Functions -- ยง1. Associated Linear Forms -- ยง2. Degenerate Theta Functions -- ยง3. Dimension of the Space of Theta Functions -- ยง4. Abelian Functions and Riemann-Roch Theorem on the Torus -- ยง5. Translations of Theta Functions -- ยง6. Projective Embedding -- VII Homomorphisms and Duality -- ยง1. The Complex and Rational Representations -- ยง2. Rational and p-adic Representations -- ยง3. Homomorphisms -- ยง4. Complete Reducibility of Poincare -- ยง5. The Dual Abelian Manifold -- ยง6. Relations with Theta Functions -- ยง7. The Kummer Pairing -- ยง8. Periods and Homology -- VIII Riemann Matrices and Classical Theta Functions -- ยง1. Riemann Matrices -- ยง2. The Siegel Upper Half Space -- ยง3. Fundamental Theta Functions -- IX Involutions and Abelian Manifolds of Quaternion Type -- ยง1. Involutions -- ยง2. Special Generators -- ยง3. Orders -- ยง4. Lattices and Riemann Forms on C2 Determined by Quaternion Algebras -- ยง5. Isomorphism Classes -- X Theta Functions and Divisors -- ยง1. Positive Divisors -- ยง2. Arbitrary Divisors -- ยง3. Existence of a Riemann Form on an Abelian Variety