Number theory, Fourier analysis and geometric discrepancy:
The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2014
|
| Series: | London Mathematical Society student texts
81 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions |
| Physical Description: | 1 Online-Ressource (x, 240 Seiten) |
| ISBN: | 9781107358379 |
| DOI: | 10.1017/CBO9781107358379 |
Staff View
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| id | DE-604.BV043940589 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781107358379 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349559 |
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| publishDate | 2014 |
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| spelling | Travaglini, Giancarlo Verfasser (DE-588)1073218651 aut Number theory, Fourier analysis and geometric discrepancy Giancarlo Travaglini, Universitá di Milano-Bicocca Number Theory, Fourier Analysis & Geometric Discrepancy Cambridge Cambridge University Press 2014 1 Online-Ressource (x, 240 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 81 The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions Number theory / Textbooks Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-04403-6 Erscheint auch als Druck-Ausgabe 978-1-107-61985-2 https://doi.org/10.1017/CBO9781107358379 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Travaglini, Giancarlo Number theory, Fourier analysis and geometric discrepancy Number theory / Textbooks Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Number theory, Fourier analysis and geometric discrepancy |
| title_alt | Number Theory, Fourier Analysis & Geometric Discrepancy |
| title_auth | Number theory, Fourier analysis and geometric discrepancy |
| title_exact_search | Number theory, Fourier analysis and geometric discrepancy |
| title_full | Number theory, Fourier analysis and geometric discrepancy Giancarlo Travaglini, Universitá di Milano-Bicocca |
| title_fullStr | Number theory, Fourier analysis and geometric discrepancy Giancarlo Travaglini, Universitá di Milano-Bicocca |
| title_full_unstemmed | Number theory, Fourier analysis and geometric discrepancy Giancarlo Travaglini, Universitá di Milano-Bicocca |
| title_short | Number theory, Fourier analysis and geometric discrepancy |
| title_sort | number theory fourier analysis and geometric discrepancy |
| topic | Number theory / Textbooks Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Number theory / Textbooks Zahlentheorie |
| url | https://doi.org/10.1017/CBO9781107358379 |
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