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Number theory, Fourier analysis and ...

Travaglini, Giancarlo.

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Number theory, Fourier analysis and geometric discrepancy

Record Type:	Electronic resources : Monograph/item
Title/Author:	Number theory, Fourier analysis and geometric discrepancy/ Giancarlo Travaglini.
remainder title:	Number Theory, Fourier Analysis & Geometric Discrepancy
Author:	Travaglini, Giancarlo.
Published:	Cambridge :Cambridge University Press, : 2014.,
Description:	x, 240 p. :ill., digital ;24 cm.
Subject:	Number theory - Textbooks. -
Online resource:	https://doi.org/10.1017/CBO9781107358379
ISBN:	9781107358379

Number theory, Fourier analysis and geometric discrepancy
Travaglini, Giancarlo.

Number theory, Fourier analysis and geometric discrepancy[electronic resource] /Number Theory, Fourier Analysis & Geometric DiscrepancyGiancarlo Travaglini. - Cambridge :Cambridge University Press,2014. - x, 240 p. :ill., digital ;24 cm. - London Mathematical Society student texts ;81. - 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.

ISBN: 9781107358379Subjects--Topical Terms:

931937
Number theory
--Textbooks.

LC Class. No.: QA241 / .T68 2014

Dewey Class. No.: 512.7

Number theory, Fourier analysis and geometric discrepancy
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100 1 $a Travaglini, Giancarlo. $3 2108935
245 1 0 $a Number theory, Fourier analysis and geometric discrepancy $h [electronic resource] / $c Giancarlo Travaglini.
246 3 $a Number Theory, Fourier Analysis & Geometric Discrepancy
260 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a x, 240 p. : $b ill., digital ; $c 24 cm.
490 1 $a London Mathematical Society student texts ; $v 81
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.
650 0 $a Number theory $v Textbooks. $3 931937
830 0 $a London Mathematical Society student texts ; $v 81. $3 3309849
856 4 0 $u https://doi.org/10.1017/CBO9781107358379