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Elementary methods in number theory

Nathanson, Melvyn B.1944-

Elementary methods in number theory

紀錄類型:	書目-電子資源 : 單行本
正題名/作者:	Elementary methods in number theory/ Melvyn B. Nathanson.
作者:	Nathanson, Melvyn B.
出版者:	New York :Springer,c 2000.
面頁冊數:	1 online resource (xviii, 513 pages).
標題:	Number theory. -
電子資源:	Click here for online access to this book (查閱全文) (EBSCO eBook)
ISBN:	0387227385 (electronic bk.)
ISBN:	9780387227382 (electronic bk.)

Elementary methods in number theory
Nathanson, Melvyn B.1944-

Elementary methods in number theory[electronic resource] /Melvyn B. Nathanson. - New York :Springer,c 2000. - 1 online resource (xviii, 513 pages). - Graduate texts in mathematics ;195. - Graduate texts in mathematics ;195..

Includes bibliographical references (p. 497-507) and index.

Cover -- Preface -- Notation and Conventions -- Table of Contents -- 1. Divisibility and Primes -- 2. Congruences -- 3. Primitive Roots and Quadratic Reciprocity -- 4. Fourier Analysis on Finite Abelian Groups -- 5. The abc Conjecture -- 6. Arithmetic Functions -- 7. Divisor Functions -- 8. Prime Numbers -- 9. The Prime Number Theorem -- 10. Primes in Arithmetic Progressions -- 11. Waring's Problem -- 12. Sums of Sequences of Polynomials -- 13. Liouville's Identity -- 14. Sums of an Even Number of Squares -- 15. Partition Asymptotics -- 16. An Inverse Theorem for Partitions -- References.

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 Erds-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.

ISBN: 0387227385 (electronic bk.)

Source: EBL219455eBook Libraryhttp://www.eblib.comSubjects--Topical Terms:

150166
Number theory.
Index Terms--Genre/Form:

172687
Electronic books.

LC Class. No.: QA241 / .N3475 2000eb

Dewey Class. No.: 512/.7

Elementary methods in number theory
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