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Number theory, Fourier analysis and ...

Travaglini, Giancarlo.

Number theory, Fourier analysis and geometric discrepancy

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Number theory, Fourier analysis and geometric discrepancyGiancarlo Travaglini.
其他題名:	Number Theory, Fourier Analysis & Geometric Discrepancy
作者:	Travaglini, Giancarlo.
出版者:	Cambridge :Cambridge University Press,2014.
面頁冊數:	x, 240 p. :ill., digital ;24 cm.
標題:	Number theory
電子資源:	https://doi.org/10.1017/CBO9781107358379
ISBN:	9781107358379$q(electronic bk.)

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: 9781107358379$q(electronic bk.)Subjects--Topical Terms:

254084
Number theory

LC Class. No.: QA241 / .T68 2014

Dewey Class. No.: 512.7

Number theory, Fourier analysis and geometric discrepancy
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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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