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Elementary Methods in Number Theory

  • Textbook
  • © 2000

Overview

Authors:
  1. Melvyn B. Nathanson

    1. Department of Mathematics, Lehman College (CUNY), Bronx, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 195)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xviii
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  2. A First Course in Number Theory

    1. Front Matter

      Pages 1-1
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    2. Divisibility and Primes

      Pages 3-43

    3. Congruences

      Pages 45-81

    4. Primitive Roots and Quadratic Reciprocity

      Pages 83-120

    5. Fourier Analysis on Finite Abelian Groups

      Pages 121-169

    6. The abc Conjecture

      Pages 171-197

  3. Divisors and Primes in Multiplicative Number Theory

    1. Front Matter

      Pages 199-199
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    2. Arithmetic Functions

      Pages 201-229

    3. Divisor Functions

      Pages 231-266

    4. Prime Numbers

      Pages 267-288

    5. The Prime Number Theorem

      Pages 289-323

    6. Primes in Arithmetic Progressions

      Pages 325-351

  4. Three Problems in Additive Number Theory

    1. Front Matter

      Pages 353-353
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    2. Waring’s Problem

      Pages 355-374

    3. Sums of Sequences of Polynomials

      Pages 375-399

    4. Liouville’s Identity

      Pages 401-421

    5. Sums of an Even Number of Squares

      Pages 423-454

    6. Partition Asymptotics

      Pages 455-474

    7. An Inverse Theorem for Partitions

      Pages 475-495
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Keywords

About this book

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.

Authors and Affiliations

  • Department of Mathematics, Lehman College (CUNY), Bronx, USA

    Melvyn B. Nathanson

Bibliographic Information

  • Book Title: Elementary Methods in Number Theory

  • Authors: Melvyn B. Nathanson

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/b98870

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Melvyn B. Nathanson 2000

  • Hardcover ISBN: 978-0-387-98912-9Published: 21 December 1999

  • Softcover ISBN: 978-1-4757-7392-7Published: 02 May 2013

  • eBook ISBN: 978-0-387-22738-2Published: 11 January 2008

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVIII, 514

  • Topics: Number Theory

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