000			01677 a2200241 4500
008			240615b |||||||| |||| 00| 0 eng d
020			_a9781470470333
082			_a516.158 ROB
100			_aRobins, Sinai
245			_aFourier analysis on polytopes and the geometry of numbers: part I: a friendly introduction
260			_aProvidence, Rhode Island: _bAmerican Mathematical Society, _c2024.
300			_axxiii, 325p.: _bcol. ill.; pbk.: _c21cm.
440			_aStudent Mathematical Library, Vol. 107
504			_aInclude bibliography & index.
520			_aThis 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. https://bookstore.ams.org/stml-107
650			_aFourier Analysis
650			_aNumber Theory
650			_aGeometry
650			_aPolytopes
650			_aLattices
650			_aConvex Bodies
942			_cTD _2ddc
999			_c60082 _d60082