Buy Books Online > Number theory > Quadratic Irrationals An Introduction to Classical Number Theory (English) (Hardcover)

# Quadratic Irrationals An Introduction to Classical Number Theory (English) (Hardcover)

**Product Details:** Share this by email:

ISBN: 9781466591837 Publisher: T&F
Year of publishing: 2013 Format: Hardcover
No of Pages: 431 Language: English

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic...Read more

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting the author focuses on equivalence continued fractions quadratic characters quadratic orders binary quadratic forms and class groups. The book highlights the connection between Gauss's theory of binary forms and the arithmetic of quadratic orders. It collects essential results of the theory that have previously been difficult to access and scattered in the literature including binary quadratic Diophantine equations and explicit continued fractions biquadratic class group characters the divisibility of class numbers by 16 F. Mertens' proof of Gauss's duplication theorem and a theory of binary quadratic forms that departs from the restriction to fundamental discriminants. The book also proves Dirichlet's theorem on primes in arithmetic progressions covers Dirichlet's class number formula and shows that every primitive binary quadratic form represents infinitely many primes. The necessary fundamentals on algebra and elementary number theory are given in an appendix. Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature the notation is far from being standardized and a unifying approach to the different aspects is lacking. Covering both classical and recent results this book unifies the theory of continued fractions quadratic orders binary quadratic forms and class groups based on the concept of a quadratic irrational.

Read less

Read less

**About the author:**Franz Halter-Koch

**Review**:

... [a] successful attempt to present a cohesive treatment of several important topics in classical number theory by first developing a theory of quadratic irrationals and then building on that to...Read more

... [a] successful attempt to present a cohesive treatment of several important topics in classical number theory by first developing a theory of quadratic irrationals and then building on that to show how the other topics reflect different faces of this theory. ... works best as a monograph for those who are already familiar with some parts of the material covered here and would like to see other approaches. ... it does include a better selection of numerical examples than is found in most books, and it has a number of applications to other areas such as diophantine equations." -Allen Stenger, MAA Reviews, January 2014 "...comprehensive text dealing with the theory of binary quadratic forms. ... one of the main interests of this book is that it gathers a lot of important results which are generally strewn throughout the literature and are quite difficult to access. This text is quite clear and some exercises and examples are scattered throughout the book. I therefore think that it will find many interested readers within the international mathematical community." - Olivier Bordelles, Mathematical Reviews Clippings, December 2013

Read less

Read less

Other books by Franz Halter-Koch

**Price**:

You save: Rs.800

Vendor : Variety Books, Delhi

**FREE SHIPPING** | Delivered in 5 working days

(Cash on delivery not available)

Imported Edition

Be assured. 7 days Return & Refund Policy.**Click here**