02976cam  22004938i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000340013305000230016708200300019008400570022010000280027724501030030526300090040826400700041730000350048733600260052233700280054833800270057649000470060350400510065050505050070150600500120653300950125653800360135158800470138765000220143465000150145665000250147165001120149665001010160865001600170965000770186965000670194665000790201365001570209277601430224985600430239285600470243523413851RPAM20240417155037.0a      b    001 0 cr/|||||||||||240417s2024    riu     ob    001 0 eng    a9781470476632 (online)  aDLCbengerdacDLCdDLCdRPAM00aQA403.5b.R63 202400a516/.158223/eng/20231213  a51M20a11P21a32A50a11H06a11H16a11H31a52B202msc1 aRobins, Sinai,eauthor.10aFourier analysis on polytopes and the geometry of numbers /h[electronic resource] cSinai Robins.  a2403 1aProvidence, Rhode Island :bAmerican Mathematical Society,c2024.  a1 online resource (volumes cm)  atextbtxt2rdacontent  aunmediatedbn2rdamedia  avolumebnc2rdacarrier0 aThe Student Mathematical Library, vv. 107  aIncludes bibliographical references and index.00tMotivational problem: Tiling a rectangle with rectanglestExamples nourish the theorytThe basics of Fourier analysistGeometry of numbers, Part I: Minkowski meets SiegeltAn introduction to Euclidean latticestGeometry of numbers, Part II: Blichfedt's theoremtThe Fourier transform of a polytope via its vertex description: Brion's theoremtWhat is an angle in higher dimensions?tAppendix A. Solutions and hints to selected problemstAppendix B. The dominated convergence theorem and other goodies1 aAccess is restricted to licensed institutions  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2024  aMode of access : World Wide Web  aDescription based on print version record. 0aFourier analysis. 0aPolytopes. 0aGeometry of numbers. 7aGeometry -- Real and complex geometry -- Polyhedra and polytopes; regular figures, division of spaces.2msc 7aNumber theory -- Additive number theory; partitions -- Lattice points in specified regions.2msc 7aSeveral complex variables and analytic spaces -- Holomorphic functions of several complex variables -- Harmonic analysis of several complex variables.2msc 7aNumber theory -- Geometry of numbers -- Lattices and convex bodies.2msc 7aNumber theory -- Geometry of numbers -- Nonconvex bodies.2msc 7aNumber theory -- Geometry of numbers -- Lattice packing and covering.2msc 7aConvex and discrete geometry -- Polytopes and polyhedra -- Lattice polytopes (including relations with commutative algebra and algebraic geometry).2msc0 iPrint version: aRobins, Sinai,tFourier analysis on polytopes and the geometry of numbers /w(DLC)   2023053408x1520-9121z97814704703334 3Contentsuhttps://www.ams.org/stml/1074 3Contentsuhttps://doi.org/10.1090/stml/107