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Advanced Number Theory with Applications
Contributor(s): Mollin, Richard A. (Author)

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ISBN: 1420083287     ISBN-13: 9781420083286
Publisher: CRC Press
OUR PRICE: $247.00  

Binding Type: Hardcover - See All Available Formats & Editions
Published: August 2009
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Annotation:

Intended for a second course at the graduate level, this book provides an advanced treatment of number theory. After an introduction to algebraic number theory, the text concentrates on ideals and quadratic forms, before moving on to Liouville's theorem, Euler's constant, and Minkowski's convex body problem and proof. Later chapters provide a more advanced view of arithmetic functions, including coverage of p-sidic analysis, Gauss sums, the Dirichlet theorem, elliptic curve crptography, Diophantine equations, and sieve methods, including Selberg's sieve and Erathosthenes sieve. A separate chapter addresses modular forms and functions.

Click for more in this series: Discrete Mathematics & Its Application

Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Mathematics | Combinatorics
- Computers | Operating Systems - General
Dewey: 512.7
LCCN: 2009026636
Series: Discrete Mathematics & Its Application
Physical Information: 1.2" H x 6.2" W x 9.3" L (1.70 lbs) 440 pages
Features: Bibliography, Illustrated, Index, Table of Contents
Review Citations: Scitech Book News 12/01/2009 pg. 35
 
Descriptions, Reviews, Etc.
Publisher Description:

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data.

With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat's Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue-Siegel-Roth theorem, Hall's conjecture, the Erdös-Mollin--Walsh conjecture, and the Granville-Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes', Selberg's, Linnik's, and Bombieri's sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring.

By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.

 
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