Probabilistic diophantine approximation : randomness in lattice point counting / Jozsef Beck.
Material type:
TextSeries: Springer monographs in mathematicsPublication details: Switzerland : Springer, 2014.Description: xvi, 487 pages : illustrations ; 25 cmISBN: - 9783319107400
- 512.73 23 B393
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 512.73 B393 (Browse shelf(Opens below)) | Available | 138015 |
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| No cover image available | No cover image available | No cover image available | ||||||
| 512.73 B168 Diophantine inequalities | 512.73 B168 Transcendental number theory | 512.73 B328 Analytic number theory : | 512.73 B393 Probabilistic diophantine approximation : | 512.73 B739 Riemann hypothesis | 512.73 C287t Theory of numbers and diophantine analysis | 512.73 C397 Diophantine approximation |
Includes bibliographical references and index.
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.
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.
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