01786nam0 22003853i 450 PUV111829520231121125621.0888801844120120406d2006 ||||0itac50 baitaitz01i xxxe z01n˜Le œorigini della Diocesi di Mantova e le sedi episcopali dell'Italia settentrionale (4.-11. secolo)a cura di Giancarlo Andenna ... [et al.]Centro di antichità altoadriatiche, Casa Bertoli AquileiaTriesteEditreg2006XXXII, 504 p.ill.24 cmAntichità altoadriatiche63Atti del Convegno tenuto a Mantova nel 2004001CFI00178722001 Antichità altoadriatiche63Mantova <diocesi>OriginiCongressi2004FIRBVEC236190IDiocesiItalia settentrionaleSec. 4.-11.Congressi2004FIRBVEC236191I282.4528CHIESA CATTOLICA ROMANA. MANTOVA (PROV.)21Brogiolo, Gian PietroCFIV063243Ardenna, GiancarloLO1V010350Salvarani, RenataRAVV054586Brogiolo, GiampietroCFIV116984Brogiolo, Gian PietroBrogiolo, Gian PieroCFIV136279Brogiolo, Gian PietroITIT-0120120406IT-FR0017 Biblioteca umanistica Giorgio ApreaFR0017 PUV1118295Biblioteca umanistica Giorgio Aprea 52MAG 4 Coll D 63 52SBA0000138235 VMN RS Scambio Centro Ant. Altoadr.A 2012040620120406 52Origini della Diocesi di Mantova e le sedi episcopali dell'Italia settentrionale (4.-11. secolo)3614846UNICAS03597nam 22006972 450 991079061200332120151005020623.01-139-89304-11-107-42515-81-107-42299-X1-107-41992-11-107-41730-91-139-62680-91-107-42114-41-107-41857-7(CKB)2550000001138789(EBL)1394585(OCoLC)858903141(SSID)ssj0000985426(PQKBManifestationID)12338352(PQKBTitleCode)TC0000985426(PQKBWorkID)10929484(PQKB)11732006(UkCbUP)CR9781139626804(Au-PeEL)EBL1394585(CaPaEBR)ebr10774095(CaONFJC)MIL538459(MiAaPQ)EBC1394585(PPN)261282190(EXLCZ)99255000000113878920121121d2013|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierLattice sums then and now /J.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[electronic resource]Cambridge :Cambridge University Press,2013.1 online resource (xix, 368 pages) digital, PDF file(s)Encyclopedia of mathematics and its applications ;volume 150Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-03990-8 1-306-07208-5 Includes bibliographical references and index.Lattice 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.The 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.Encyclopedia of mathematics and its applications ;v. 150.Lattice Sums Then & NowLattice theoryNumber theoryLattice theory.Number theory.511.3/3MAT022000bisacshBorwein Jonathan M.55373UkCbUPUkCbUPBOOK9910790612003321Lattice sums then and now3717651UNINA