Arithmetic of Algebraic Curves

by Serguei A. Stepanov

Overview

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 over 250 excercises 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.

Product Details

ISBN-13:	9780306110368
Publisher:	Springer US
Publication date:	12/31/1994
Series:	Monographs in Contemporary Mathematics
Edition description:	1995
Pages:	422
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

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.

Editorial Reviews

Deals with the theory of equations in two variables and arithmetic, algebraic-geometric, and logical aspects of the problem. Covers equations over finite fields, distribution of quadratic residues and nonresidues, the Riemann-Roch theorem, integral points on curves, the Siegel-Mahler theorem, and Hilbert's tenth problem. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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