Arifmetika Algebraicheskikh Krivykh

Name: Arifmetika Algebraicheskikh Krivykh
Price: 445.35 USD
Availability: InStock
ISBN: 9780306110368

ISBN-10: 0306110369

ISBN-13: 9780306110368

Edition: 1995

Authors: Serguei A. Stepanov

List price: $449.99

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Description:

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.

Book details

List price: $449.99
Copyright year: 1995
Publisher: Springer
Publication date: 12/31/1994
Binding: Hardcover
Pages: 422
Size: 6.14" wide x 9.21" long x 1.00" tall
Weight: 3.850
Language: English



Introduction


Equations over Finite Fields


Congruences


Congruences Relative to a Double Module and Finite Fields


Artin's L-Functions


Superelliptic Equations and the Artin- Schreier Equation


Distribution of Quadratic Residues and Nonresidues


The Results of Vinogradov and Burgess


The Large Sieve and its Application to the Least Quadratic Nonresidue Problem


Rational Points on Algebraic Curves


Rational Curves


Elliptic Curves


The Riemann-Roch Theorem


Affine and Projective Varieties


Divisors of Algebraic Curves


The Riemann-Roch Theorem on an Algebraic Curve


The Riemann Hypothesis for Congruence Zeta-Functions


Zeta Functions of Algebraic Curves and Varieties


The Number of Rational Points of an Algebraic Curve over a Finite Field


Integral Points on Curves and Nonstandard Arithmetic


Integral Points on Algebraic Curves


Algebraic Systems and Models


Enlargements of Algebraic Number Fields


The Siegel-Mahler Theorem


A Nonstandard Equivalent of the Siegel-Mahler Theorem


Proof of the Siegel-Mahler Theorem


Appendix. Hilbert's Tenth Problem


References


Index