LEADER 03597nam 22006972 450 001 9910823442903321 005 20151005020623.0 010 $a1-139-89304-1 010 $a1-107-42515-8 010 $a1-107-42299-X 010 $a1-107-41992-1 010 $a1-107-41730-9 010 $a1-139-62680-9 010 $a1-107-42114-4 010 $a1-107-41857-7 035 $a(CKB)2550000001138789 035 $a(EBL)1394585 035 $a(OCoLC)858903141 035 $a(SSID)ssj0000985426 035 $a(PQKBManifestationID)12338352 035 $a(PQKBTitleCode)TC0000985426 035 $a(PQKBWorkID)10929484 035 $a(PQKB)11732006 035 $a(UkCbUP)CR9781139626804 035 $a(Au-PeEL)EBL1394585 035 $a(CaPaEBR)ebr10774095 035 $a(CaONFJC)MIL538459 035 $a(MiAaPQ)EBC1394585 035 $a(PPN)261282190 035 $a(EXLCZ)992550000001138789 100 $a20121121d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLattice sums then and now /$fJ.M. Borwein, University of Newcastle, New South Wales, M.L. Glasser, Clarkson University, New York R.C. Mcphedran, University of Sydney, J.G. Wan, University of Newcastle, New South Wales, I.J. Zucker, King's College London$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (xix, 368 pages) $cdigital, PDF file(s) 225 1 $aEncyclopedia of mathematics and its applications ;$vvolume 150 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-03990-8 311 $a1-306-07208-5 320 $aIncludes bibliographical references and index. 327 $aLattice sums -- Convergence of lattice sums and Madelung's constant -- Angular lattice sums -- Use of Dirichlet series with complex characters -- Lattice sums and Ramanujan's modular equations -- Closed form evaluations of three- and four-dimensional sums -- Electron sums -- Madelung sums in higher dimensions -- Seventy years of the Watson integrals. 330 $aThe study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered. 410 0$aEncyclopedia of mathematics and its applications ;$vv. 150. 517 3 $aLattice Sums Then & Now 606 $aLattice theory 606 $aNumber theory 615 0$aLattice theory. 615 0$aNumber theory. 676 $a511.3/3 686 $aMAT022000$2bisacsh 700 $aBorwein$b Jonathan M.$055373 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910823442903321 996 $aLattice sums then and now$94064090 997 $aUNINA