Number Theory, Fourier Analysis and Geometric Discrepancy - Giancarlo Travaglini

Number Theory, Fourier Analysis and Geometric Discrepancy

Buch | Hardcover
252 Seiten
2014
Cambridge University Press (Verlag)
978-1-107-04403-6 (ISBN)
153,35 inkl. MwSt
Geometric discrepancy theory is a rapidly growing modern field. This book provides a complete introduction to the topic with exposition based on classical number theory and Fourier analysis, but assuming no prior knowledge of either. Ideal as a guide to the subject for advanced undergraduate or beginning graduate students.
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.

Giancarlo Travaglini is Professor of Mathematics at the University of Milano-Bicocca. He is the author of numerous research papers and several books in the areas of abstract harmonic analysis, Fourier analysis and discrepancy theory. He is a member of the Unione Matematica Italiana and the American Mathematical Society. His current mathematical interests include Fourier analysis, discrepancy theory, radon transforms and didactics of mathematics.

Part I. Elementary Number Theory: 1. Prelude; 2. Arithmetic functions and integer points; 3. Congruences; 4. Quadratic reciprocity and Fourier series; 5. Sums of squares; Part II. Fourier Analysis and Geometric Discrepancy: 6. Uniform distribution and completeness of the trigonometric system; 7. Discrepancy and trigonometric approximation; 8. Integer points and Poisson summation formula; 9. Integer points and exponential sums; 10. Geometric discrepancy and decay of Fourier transforms; 11. Discrepancy in high dimension and Bessel functions; References; Index.

Erscheint lt. Verlag 12.6.2014
Reihe/Serie London Mathematical Society Student Texts
Zusatzinfo Worked examples or Exercises; 1 Tables, black and white; 6 Halftones, unspecified; 16 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 152 x 229 mm
Gewicht 470 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-107-04403-0 / 1107044030
ISBN-13 978-1-107-04403-6 / 9781107044036
Zustand Neuware
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