Probabilistic diophantine approximation: randomness in lattice point counting
by Beck, Jozsef
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to e…
Read More ↓Title Statements
- Full title :Probabilistic diophantine approximation : randomness in lattice point counting / József Beck.
Summary
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques. Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
Read More ↓Edition Statements
- Publication Date:©2014.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham
- Language:eng
- Publication Date:©2014.
The Physical Object
- Description:xvi, 487 pages : : illustrations ; : 25 cm
Edition Identifiers
- ISBN:9783319107400, 3319107402
- oclc:ocn886485517
- LC Classification:QA242
- Dewey Decimal:512.7/3
Table of Contents
1. What is "probabilistic" diophantine approximation? -- 2. Expectation and its connection with quadratic fields -- 3. Variance and its connection with quadratic fields -- 4. Proving randomness -- 5. Pell's equation, superirregularity and randomness -- 6. More on randomness.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Nevanlinna theory in several complex variables and diophantine approximation
Noguchi, Junjiro
Nevanlinna theory in several complex variables and Diophantine approximation
Noguchi, Junjiro
Probabilistic diophantine approximation: randomness in lattice point counting
Beck, Jozsef
Probabilistic diophantine approximation: randomness in lattice point counting
Beck, Jozsef
Four Faces of Number Theory
Metric Diophantine Approximation on Manifolds
Metric diophantine approximation on manifolds
Files & Downloads
-
Probabilistic Diophantine Approximation: Randomne…
PDF · 3.0 MB · updated -
Probabilistic Diophantine Approximation: Randomne…
PDF · 5.1 MB · updated
Rate & Review