Lattice Sums Then and Now 1st Edition by J M Borwein,M L Glasser,R C McPhedran,J G Wan,I J Zucker ISBN 1107039908 978-1107039902

Lattice Sums Then and Now 1st Edition by J. M. Borwein, M. L. Glasser, R. C. McPhedran, J. G. Wan, I. J. Zucker – Ebook PDF Instant Download/Delivery: 1107039908, 978-1107039902

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Product details:

ISBN 10: 1107039908 

ISBN 13: 978-1107039902

Author: J. M. Borwein, M. L. Glasser, R. C. McPhedran, J. G. Wan, I. J. Zucker

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.

Table of contents:

Chapter 1 Lattice sums
Chapter 2 Convergence of lattice sums and Madelung’s constant
Chapter 3 Angular lattice sums
Chapter 4 Use of Dirichlet series with complex characters
Chapter 5 Lattice sums and Ramanujan’s modular equations
Chapter 6 Closed-form evaluations of three- and four-dimensional sums
Chapter 7 Electron sums
Chapter 8 Madelung sums in higher dimensions
Chapter 9 Seventy years of the Watson integrals

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Tags: J M Borwein, M L Glasser, R C McPhedran, J G Wan, I J Zucker, Lattice Sums, Then and Now