ENGLISH

Fourier Analysis on Polytopes and the Geometry of Numbers - Part I: A Friendly Introduction

By Sinai Robins

Book information

Publisher
American Mathematical Society
Year
2024
ISBN
9781470470333, 9781470476632
LCC
QA403.5 .R63 2024
Language
english
Format
DJVU
Filesize
4 MB (4100760 bytes)
Series
Student Mathematical Library 107
Volume
1
Edition
1
Pages
325\352
Topic
Mathematics\\Number Theory
DPI
400
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2024-06-04 10:18:08
Blichfeldt's TheoremBrion's TheoremFourier AnalysisLatticesPolytopes

Description

This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.

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