000			02749nam a22003738i 4500
001			CR9781139626804
003			UkCbUP
005			20200124160211.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			121121s2013||||enk o ||1 0|eng|d
020			_a9781139626804 (ebook)
020			_z9781107039902 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA171.5 _b.B67 2013
082	0	0	_a511.3/3 _223
100	1		_aBorwein, Jonathan M., _eauthor.
245	1	0	_aLattice sums then and now / _cJ.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.
246	3		_aLattice Sums Then & Now
264		1	_aCambridge : _bCambridge University Press, _c2013.
300			_a1 online resource (xix, 368 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 150
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_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.
520			_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.
650		0	_aLattice theory.
650		0	_aNumber theory.
776	0	8	_iPrint version: _z9781107039902
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 150.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139626804
999			_c515868 _d515866