Quadratic Irrationals

Regular price €68.99
Regular price €69.99 Sale Sale price €68.99
A01=Franz Halter-Koch
Age Group_Uncategorized
Age Group_Uncategorized
Ambiguous Pair
Author_Franz Halter-Koch
automatic-update
binary
Binary Quadratic Forms
Biquadratic Residue
Category1=Non-Fiction
Category=PBD
Category=PBF
Category=PBH
Category=PBV
Character Modulo
Class Semigroup
Continued Fractions
COP=United Kingdom
Delivery_Pre-order
Diophantine Equation
discriminant
Distinct Odd Primes
eq_isMigrated=2
eq_new_release
equation
form
function
fundamental
Fundamental Discriminant
Gauss Sum
holomorphic
Integral Squares
Jacobi Symbol
Language_English
modulo
Non-zero Ideal
Odd Prime
PA=Not yet available
Partial Denominators
pell's
Pell’s Equation
Pn Qn
Price_€50 to €100
Properly Equivalent
PS=Forthcoming
Quadratic Discriminant
Quadratic Irrationals
Quadratic Orders
Quadratic Reciprocity Law
Quadratic Residue
Quadratic Residue Modulo
residue
Residue Modulo
softlaunch

Product details

  • ISBN 9781032919973
  • Weight: 453g
  • Dimensions: 178 x 254mm
  • Publication Date: 14 Oct 2024
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Paperback
  • Language: English
Delivery/Collection within 10-20 working days

Our Delivery Time Frames Explained
2-4 Working Days: Available in-stock

10-20 Working Days
: On Backorder

Will Deliver When Available
: On Pre-Order or Reprinting

We ship your order once all items have arrived at our warehouse and are processed. Need those 2-4 day shipping items sooner? Just place a separate order for them!

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.

Franz Halter-Koch retired as a professor of mathematics from the University of Graz in 2004. A member of the Austrian Academy of Science, Dr. Halter-Koch is the author/coauthor of roughly 150 scientific articles, author of Ideal Systems: An Introduction to Multiplicative Ideal Theory, and coauthor of Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory. His research focuses on elementary and algebraic number theory, non-unique factorizations, and abstract multiplicative ideal theory.