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" Arithmetic of algebraic curves / "
Serguei A. Stepanov ; translated fom Russian by Irene Aleksanova.
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BL
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| Record Number
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997281
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| Doc. No
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b751651
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| Uniform Title
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Arifmetika algebraicheskikh krivykh.English
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| Main Entry
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Stepanov, S. A., (Sergeĭ Aleksandrovich)
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| Title & Author
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Arithmetic of algebraic curves /\ Serguei A. Stepanov ; translated fom Russian by Irene Aleksanova.
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| Publication Statement
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New York :: Consultants Bureau,, ©1994.
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| Series Statement
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Monographs in contemporary mathematics
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| Page. NO
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xii, 422 pages :: illustrations ;; 26 cm.
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| ISBN
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0306110369
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: 9780306110368
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| Bibliographies/Indexes
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Includes bibliographical references (pages 391-413) and index.
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| Contents
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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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| Subject
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Curves, Algebraic.
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Curves, Elliptic.
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Diophantine equations.
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Analyse diophantienne.
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Courbes algébriques.
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Courbes elliptiques.
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Curves, Algebraic.
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Curves, Elliptic.
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Diophantine equations.
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Algebraische Kurve.
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Algebraische Kurve.
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Arithmetik.
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Arithmetik.
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Diophantische Gleichung.
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Diophantische Gleichung.
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Algebraïsche krommen.
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Diofantische vergelijkingen.
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| Dewey Classification
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512/.72
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| LC Classification
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QA567.S82513 1994
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| NLM classification
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17,1ssgn
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31.14bcl
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31.51bcl
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MAT 145fstub
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SK 240rvk
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