Lattice Sums: Then and Now

Lattice Sums: Then and Now (Authors’ Website)

Volume 150 of Encyclopedia of Mathematics and its Applications     

  •  J. M. Borwein, University of Newcastle, New South Walescover
  •  M. L. Glasser, Clarkson University, New York
  •  R. C. McPhedran, University of Sydney
  •  J. G. Wan, Singapore University of Technology and Design
  •  I. J. Zucker, Kings College, London
  •  PUBLISHED:  August 1 2013
  •  FORMAT: Hardback
  •  ISBN: 9781107039902

 From the CUP website: 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.

  •  Expands and updates the seminal paper written by two of the book’s authors, M. L. Glasser   and I. J. Zucker
  •  Will be of value to both experienced practitioners and those new to the field
  •  Assembles results that were scattered across the literature and often underexploited

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