Arithmetic of Algebraic Curves

1995
ISBN: 978-0-306-11036-8
Verlag: Springer US

Buch, Englisch, 422 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1750 g

Reihe: Monographs in Contemporary Mathematics

Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.

Zielgruppe

Research

Autoren/Hrsg.

Stepanov, Serguei A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Equations over Finite Fields. Distribution of Quadratic Residues and Nonresidues. Historical Commentaries on Chapters 1 and 2. Rational Points on Algebraic Curves. The Riemann-Roch Theorem. The Riemann Hypothesis for Congruence Zetafunctions. Integral Points on Curves and Nonstandard Arithmetic. The Siegel-Mahler Theorem. Appendix: Hilbert's Tenth Problem. Index.