عنوان

Arithmetic of algebraic curves /

0306110369

9780306110368

b751651

Arithmetic of algebraic curves /

[Book]

Serguei A. Stepanov ; translated fom Russian by Irene Aleksanova.

New York :

Consultants Bureau,

©1994.

xii, 422 pages :

illustrations ;

26 cm.

Monographs in contemporary mathematics

Includes bibliographical references (pages 391-413) and index.

Ch. 1. Equations over Finite Fields. 1.1. Congruences. 1.2. Congruences Relative to a Double Module and Finite Fields. 1.3. Artin's L-Functions. 1.4. Superelliptic Equations and the Artin- Schreier Equation -- Ch. 2. Distribution of Quadratic Residues and Nonresidues. 2.1. The Results of Vinogradov and Burgess. 2.2. The Large Sieve and its Application to the Least Quadratic Nonresidue Problem -- Ch. 3. Rational Points on Algebraic Curves. 3.1. Rational Curves. 3.2. Elliptic Curves -- Ch. 4. The Riemann-Roch Theorem. 4.1. Affine and Projective Varieties. 4.2. Divisors of Algebraic Curves. 4.3. The Riemann-Roch Theorem on an Algebraic Curve -- Ch. 5. The Riemann Hypothesis for Congruence Zeta-Functions. 5.1. Zeta Functions of Algebraic Curves and Varieties. 5.2. The Number of Rational Points of an Algebraic Curve over a Finite Field -- Ch. 6. Integral Points on Curves and Nonstandard Arithmetic. 6.1. Integral Points on Algebraic Curves. 6.2. Algebraic Systems and Models -- 6.3. Enlargements of Algebraic Number Fields -- Ch. 7. The Siegel-Mahler Theorem. 7.1. A Nonstandard Equivalent of the Siegel-Mahler Theorem. 7.2. Proof of the Siegel-Mahler Theorem -- Appendix. Hilbert's Tenth Problem.

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Arifmetika algebraicheskikh krivykh.

English

Curves, Algebraic.

Curves, Elliptic.

Diophantine equations.

Algebraïsche krommen.

Algebraische Kurve.

Algebraische Kurve.

Analyse diophantienne.

Arithmetik.

Arithmetik.

Courbes algébriques.

Courbes elliptiques.

Curves, Algebraic.

Curves, Elliptic.

Diofantische vergelijkingen.

Diophantine equations.

Diophantische Gleichung.

Diophantische Gleichung.

Stepanov, S. A., (Sergeĭ Aleksandrovich)

20201204112122.0

[Book]

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