An Introduction to Number Theory

Couverture
Springer Science & Business Media, 24 nov. 2005 - 297 pages

An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject.

In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory.

A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.

Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to learn some of the big ideas in number theory.

 

Pages sélectionnées

Table des matières

Contents
1
Diophantine Equations
43
Quadratic Diophantine Equations
59
Recovering the Fundamental Theorem of Arithmetic
83
Elliptic Curves
93
Elliptic Functions 121
120
Heights
133
The Riemann Zeta Function
157
The Functional Equation of
182
Primes in an Arithmetic Progression
207
Converging Streams
225
Computational Number Theory
245
References
279
Index
287
Droits d'auteur

Autres éditions - Tout afficher

An Introduction to Number Theory
G. Everest,Thomas Ward
Aperçu limité - 2007
An Introduction to Number Theory
G. Everest,Thomas Ward
Aucun aperçu disponible - 2007

Expressions et termes fréquents

Abelian group arithmetic function assume binary bound Carmichael number chapter completes the proof complex compute congruence congruent number conjecture converges coprime Corollary curve y2 deduce defined Definition denominator denote Diophantine Dirichlet Dirichlet character divides elements elliptic curve Euclid’s Euclidean Algorithm Euler product Example Exercise Fermat’s Little Theorem finite first follows Fourier Fundamental Theorem gcd(a gives greatest common divisor ideals in OK inequality infinitely integral solutions L-function Legendre symbol Lemma logn Mersenne Mersenne primes method modulo multiplicative nontrivial nonzero number theory odd prime polynomial primality testing prime factors Prime Number Theorem primitive divisor problem proof of Theorem prove quadratic form quadratic residue rational point result Riemann Hypothesis Riemann zeta function right-hand side ring Section sequence simple pole square square-free integer Summation Formula Suppose Theorem of Arithmetic torsion points values write zero

Informations bibliographiques

TitreAn Introduction to Number Theory
Volume 232 de Graduate Texts in Mathematics
AuteursG. Everest, Thomas Ward
Éditionillustrée
ÉditeurSpringer Science & Business Media, 2005
ISBN1846280443, 9781846280443
Longueur297 pages
  
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