Number Theory, Fourier Analysis and Geometric Discrepancy (Hardcover) (ISBN-13: 9781107044036)

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.

Author: Giancarlo Travaglini
ISBN-10: 1107044030
ISBN-13: 9781107044036
Publisher: Cambridge University Press
Language: English
Published: 06/12/2014
Pages: 252
Format: Hardcover
Weight: 1.05lbs
Size: 9.00h x 5.80w x 0.70d