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A comprehensive course in number theory /
"Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [UK] ; New York :
Cambridge University Press,
2012.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Baker, Alan, |d 1939- |e author. | |
| 245 | 1 | 2 | |a A comprehensive course in number theory / |c Alan Baker. |
| 264 | 1 | |a Cambridge [UK] ; |a New York : |b Cambridge University Press, |c 2012. | |
| 264 | 4 | |c ©2012 | |
| 300 | |a 1 online resource (xv, 251 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 520 | |a "Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy-Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies"-- |c Provided by publisher. | ||
| 504 | |a Includes bibliographical references (pages 240-245) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Divisibility -- Arithmetical functions -- Congruences -- Quadratic residues -- Quadratic forms -- Diophantine approximation -- Quadratic fields -- Diophantine equations -- Factorization and primality testing -- Number fields -- Ideals -- Units and ideal classes -- Analytic number theory -- On the zeros of the zeta-function -- On the distribution of the primes -- The sieve and circle methods -- Elliptic curves. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Number theory |v Textbooks. | |
| 650 | 7 | |a MATHEMATICS |x Number Theory. |2 bisacsh | |
| 650 | 0 | 7 | |a Números , Teoría de |2 embucm |
| 650 | 7 | |a Number theory |2 fast | |
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| 655 | 7 | |a Textbooks |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Baker, Alan, 1939- |t Comprehensive course in number theory. |d Cambridge, UK ; New York : Cambridge University Press, 2012 |z 9781107019010 |w (DLC) 2012013414 |w (OCoLC)792941483 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473241 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- A Comprehensive Course in Number Theory -- Title -- Copyright -- Contents -- Preface -- Introduction -- Gauss and Number Theory -- 1 Divisibility -- 1.1 Foundations -- 1.2 Division algorithm -- 1.3 Greatest common divisor -- 1.4 Euclid's algorithm -- 1.5 Fundamental theorem -- 1.6 Properties of the primes -- 1.7 Further reading -- 1.8 Exercises -- 2 Arithmetical functions -- 2.1 The function [x] -- 2.2 Multiplicative functions -- 2.3 Euler's (totient) function ø(n) -- 2.4 The Möbius function μ(n) -- 2.5 The functions τ(n) and σ(n) -- 2.6 Average orders -- 2.7 Perfect numbers -- 2.8 The Riemann zeta-function -- 2.9 Further reading -- 2.10 Exercises -- 3 Congruences -- 3.1 Definitions -- 3.2 Chinese remainder theorem -- 3.3 The theorems of Fermat and Euler -- 3.4 Wilson's theorem -- 3.5 Lagrange's theorem -- 3.6 Primitive roots -- 3.7 Indices -- 3.8 Further reading -- 3.9 Exercises -- 4 Quadratic residues -- 4.1 Legendre's symbol -- 4.2 Euler's criterion -- 4.3 Gauss' lemma -- 4.4 Law of quadratic reciprocity -- 4.5 Jacobi's symbol -- 4.6 Further reading -- 4.7 Exercises -- 5 Quadratic forms -- 5.1 Equivalence -- 5.2 Reduction -- 5.3 Representations by binary forms -- 5.4 Sums of two squares -- 5.5 Sums of four squares -- 5.6 Further reading -- 5.7 Exercises -- 6 Diophantine approximation -- 6.1 Dirichlet's theorem -- 6.2 Continued fractions -- 6.3 Rational approximations -- 6.4 Quadratic irrationals -- 6.5 Liouville's theorem -- 6.6 Transcendental numbers -- 6.7 Minkowski's theorem -- 6.8 Further reading -- 6.9 Exercises -- 7 Quadratic fields -- 7.1 Algebraic number fields -- 7.2 The quadratic field -- 7.3 Units -- 7.4 Primes and factorization -- 7.5 Euclidean fields -- 7.6 The Gaussian field -- 7.7 Further reading -- 7.8 Exercises -- 8 Diophantine equations -- 8.1 The Pell equation -- 8.2 The Thue equation -- 8.3 The Mordell equation. | |
| 880 | 8 | |6 505-00/(S |a 8.4 The Fermat equation -- 8.5 The Catalan equation -- 8.6 The abc-conjecture -- 8.7 Further reading -- 8.8 Exercises -- 9 Factorization and primality testing -- 9.1 Fermat pseudoprimes -- 9.2 Euler pseudoprimes -- 9.3 Fermat factorization -- 9.4 Fermat bases -- 9.5 The continued-fraction method -- 9.6 Pollard's method -- 9.7 Cryptography -- 9.8 Further reading -- 9.9 Exercises -- 10 Number fields -- 10.1 Introduction -- 10.2 Algebraic numbers -- 10.3 Algebraic number fields -- 10.4 Dimension theorem -- 10.5 Norm and trace -- 10.6 Algebraic integers -- 10.7 Basis and discriminant -- 10.8 Calculation of bases -- 10.9 Further reading -- 10.10 Exercises -- 11 Ideals -- 11.1 Origins -- 11.2 Definitions -- 11.3 Principal ideals -- 11.4 Prime ideals -- 11.5 Norm of an ideal -- 11.6 Formula for the norm -- 11.7 The different -- 11.8 Further reading -- 11.9 Exercises -- 12 Units and ideal classes -- 12.1 Units -- 12.2 Dirichlet's unit theorem -- 12.3 Ideal classes -- 12.4 Minkowski's constant -- 12.5 Dedekind's theorem -- 12.6 The cyclotomic field -- 12.7 Calculation of class numbers -- 12.8 Local fields -- 12.9 Further reading -- 12.10 Exercises -- 13 Analytic number theory -- 13.1 Introduction -- 13.2 Dirichlet series -- 13.3 Tchebychev's estimates -- 13.4 Partial summation formula -- 13.5 Mertens' results -- 13.6 The Tchebychev functions -- 13.7 The irrationality of ζ(3) -- 13.8 Further reading -- 13.9 Exercises -- 14 On the zeros of the zeta-function -- 14.1 Introduction -- 14.2 The functional equation -- 14.3 The Euler product -- 14.4 On the logarithmic derivative of ζ(s) -- 14.5 The Riemann hypothesis -- 14.6 Explicit formula for ζ'(s)/ζ(s) -- 14.7 On certain sums -- 14.8 The Riemann-von Mangoldt formula -- 14.9 Further reading -- 14.10 Exercises -- 15 On the distribution of the primes -- 15.1 The prime-number theorem. | |
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