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LEADER 03753cam 2200529 i 4500

001 ocn833145010;

003 OCoLC;

005 20141212064130.0;

008 130326s2013 enk b 001 0 eng ;

010 a| 2013002993;

020 a| 9781107039902 (hardback);

020 a| 1107039908 (hardback);

020 a| 9781306072083 (MyiLibrary);

020 a| 1306072085 (MyiLibrary);

020 a| 9781107418578 (e-book);

020 a| 1107418577 (e-book);

035 a| (Sirsi) 40023279040;

035 a| 40023279040;

035 a| (OCoLC)833145010;

042 a| pcc;

050 00 a| QA171.5b| .B67 2013;

082 00 a| 511.3/32| 23;

084 a| MAT0220002| bisacsh;

100 1 a| Borwein, Jonathan M.=| ^A390897;

245 10 a| Lattice sums then and now /c| 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.;

264 1 a| Cambridge :b| Cambridge University Press,c| 2013.;

300 a| xix, 368 pages ;c| 24 cm.;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

490 1 a| Encyclopedia of mathematics and its applications ;v| 150;

520 a| "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"--c| Provided by publisher.;

504 a| Includes bibliographical references (pages [350]-362) and index.;

505 0 a| 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.;

650 0 a| Lattice theory.=| ^A38115;

650 0 a| Number theory.=| ^A22877;

650 7 a| MATHEMATICS / Number Theory.2| bisacsh;

650 7 a| Lattice theory.2| fast0| (OCoLC)fst00993426;

650 7 a| Number theory.2| fast0| (OCoLC)fst01041214;

830 0 a| Encyclopedia of mathematics and its applications ;v| v. 150.=| ^A86469;

949 i| 30372013824468o| jjlm;

960 o| 1s| 120.00t| Joyner48u| JAPPz| USD;

596 a| 1;

998 a| 3450880;

999 a| QA171.5 .B67 2013w| LCc| 1i| 30372013824468d| 9/1/2014e| 4/2/2014l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 3/31/2014x| BOOKz| JSTACKSo| .STAFF. jjlm;

Lattice 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.

Author/creator	Borwein, Jonathan M.
Format	Book
Publication	Cambridge : Cambridge University Press, 2013.
Description	xix, 368 pages ; 24 cm.
Subjects	Lattice theory. Number theory.

Series	Encyclopedia of mathematics and its applications ; 150 Encyclopedia of mathematics and its applications ; v. 150. ^A86469
Contents	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.
Abstract	"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"-- Provided by publisher.
Abstract	"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)"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages [350]-362) and index.
LCCN	2013002993
ISBN	9781107039902 (hardback)
ISBN	1107039908 (hardback)
ISBN	9781306072083 (MyiLibrary)
ISBN	1306072085 (MyiLibrary)
ISBN	9781107418578 (e-book)
ISBN	1107418577 (e-book)

Lattice 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.

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