# Download e-book for kindle: Lattice Sums Then and Now (Encyclopedia of Mathematics and by J. M. Borwein,M. L. Glasser,R. C. McPhedran

By J. M. Borwein,M. L. Glasser,R. C. McPhedran

The learn of lattice sums begun while early investigators desired to cross from mechanical homes of crystals to the homes of the atoms and ions from which they have been outfitted (the literature of Madelung's constant). A parallel literature used to be outfitted round the optical homes of standard lattices of atoms (initiated by way of Lord Rayleigh, Lorentz and Lorenz). For over a century many recognized scientists and mathematicians have delved into the homes of lattices, occasionally unwittingly duplicating the paintings in their predecessors. the following, ultimately, is a entire evaluation of the gigantic physique of information that exists on lattice sums and their purposes. The authors additionally offer commentaries on open questions, and clarify smooth recommendations which simplify the duty of discovering new leads to this interesting and ongoing box. Lattice sums in a single, , 3, 4 and better dimensions are covered.

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