A01=Jorn Steuding
abc conjecture research
advanced diophantine problem solving
Algebraic Numbers
approximation
Author_Jorn Steuding
Category=PBD
Category=PBH
Category=PBM
Category=PBV
continued
Continued Fraction
Continued Fraction Expansion
Diophantine Analysis
Diophantine Approximations
Diophantine Equation
Elliptic Curve
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
equation
Euclidean Algorithm
expansion
factoring algorithms
Fermat Curve
Fermat Equation
fraction
Hensel's Lemma
Hensel’s Lemma
integer
Integer Solutions
Linear Diophantine Equation
Liouville's Theorem
Liouville’s Theorem
LLL
Minimal Polynomial
Non-trivial Solutions
Nontrivial Solutions
number
number theory methods
p-adic analysis
Partial Quotients
Pell Equation
Pn Qn
positive
Positive Integer
prime
Pythagorean Triples
Quadratic Irrationals
Quadratic Residue Mod
rational
rational approximation techniques
transcendental number theory
Product details
- ISBN 9780367392857
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 05 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain.
Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers.
Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.
Steuding, Jorn
