Number Theory, Fourier Analysis and Geometric Discrepancy (London Mathematical Society Student Texts Book 81) 1st Edition by Giancarlo Travaglini (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book shows a unique combination of the three topics. This is surely interesting and useful, but the results are not easy: the last chapters, in particular, require a certain amount of work to be properly understood. Every chapter is completed with exercises of different difficulties (ranging from easy to quite hard to proove). In conclusion, a very interesting book that won’t show its “secrets” easily

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