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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
|
| Schriftenreihe: | London Mathematical Society student texts
81 |
| Links: | https://doi.org/10.1017/CBO9781107358379 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (x, 240 Seiten) |
| ISBN: | 9781107358379 |
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| 245 | 1 | 0 | |a Number theory, Fourier analysis and geometric discrepancy |c Giancarlo Travaglini, Universitá di Milano-Bicocca |
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| 520 | |a 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. | ||
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| spelling | Travaglini, Giancarlo 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 c cr 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. Erscheint auch als Druck-Ausgabe 9781107044036 Erscheint auch als Druck-Ausgabe 9781107619852 |
| spellingShingle | Travaglini, Giancarlo Number theory, Fourier analysis and geometric discrepancy |
| 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 |
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