{"id":5716,"date":"2013-07-29T15:44:00","date_gmt":"2013-07-29T23:44:00","guid":{"rendered":"http:\/\/experimentalmath.info\/blog\/?p=5716"},"modified":"2013-07-29T15:47:00","modified_gmt":"2013-07-29T23:47:00","slug":"lattice-sums-then-and-now","status":"publish","type":"post","link":"https:\/\/experimentalmath.info\/blog\/2013\/07\/lattice-sums-then-and-now\/","title":{"rendered":"Lattice Sums: Then and Now"},"content":{"rendered":"<h2>Lattice Sums: Then and Now (Authors&#8217;\u00a0<a href=\"http:\/\/www.carma.newcastle.edu.au\/LatticeSums\/\">Website<\/a>)<\/h2>\n<h2>Volume <strong>150 of\u00a0<\/strong><a href=\"http:\/\/www.cambridge.org\/us\/academic\/subjects\/mathematics\/series\/encyclopedia-mathematics-and-its-applications\">Encyclopedia of Mathematics and its Applications<\/a>\u00a0 \u00a0 \u00a0<strong><span style=\"text-decoration: underline;\"><br \/>\n<\/span><\/strong><\/h2>\n<div>\n<ul>\n<li>\u00a0J. M. Borwein,\u00a0University of Newcastle, New South Wales<a href=\"https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-5718\" alt=\"cover\" src=\"https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover.jpg\" width=\"240\" height=\"363\" srcset=\"https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover.jpg 429w, https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover-198x300.jpg 198w, https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover-99x150.jpg 99w, https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover-400x604.jpg 400w, https:\/\/experimentalmath.info\/blog\/wp-content\/uploads\/2013\/07\/cover-199x300.jpg 199w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a><\/li>\n<li>\u00a0M. L. Glasser,\u00a0Clarkson University, New York<\/li>\n<li>\u00a0R. C. McPhedran,\u00a0University of Sydney<\/li>\n<li>\u00a0J. G. Wan,\u00a0Singapore University of Technology and Design<\/li>\n<li>\u00a0I. J. Zucker, Kings College, London<\/li>\n<\/ul>\n<\/div>\n<ul>\n<li>\u00a0PUBLISHED: \u00a0<em>August 1 2013<\/em><\/li>\n<li>\u00a0FORMAT:\u00a0Hardback<\/li>\n<li>\u00a0ISBN:\u00a09781107039902<\/li>\n<\/ul>\n<p><strong>\u00a0From the <a href=\"http:\/\/www.cambridge.org\/us\/academic\/subjects\/mathematics\/number-theory\/lattice-sums-then-and-now\">CUP website<\/a><\/strong><a href=\"http:\/\/www.cambridge.org\/us\/academic\/subjects\/mathematics\/number-theory\/lattice-sums-then-and-now\">: <\/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&#8217;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.<\/p>\n<div>\n<ul>\n<li>\u00a0Expands and updates the seminal paper written by two of the book&#8217;s authors, M. L. Glasser \u00a0 and I. J. Zucker<\/li>\n<li>\u00a0Will be of value to both experienced practitioners and those new to the field<\/li>\n<li>\u00a0Assembles results that were scattered across the literature and often underexploited<\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Lattice Sums: Then and Now (Authors&#8217; Website) Volume 150 of Encyclopedia of Mathematics and its Applications 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, Singapore University of Technology and Design I. J. Zucker, Kings College, London PUBLISHED: August 1 2013 FORMAT: Hardback ISBN: 9781107039902 <\/p>\n<p> 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&#8217;s <\/p>\n<p>Continue reading <a href=\"https:\/\/experimentalmath.info\/blog\/2013\/07\/lattice-sums-then-and-now\/\">Lattice Sums: Then and Now<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-5716","post","type-post","status-publish","format-standard","hentry","category-essays","odd"],"_links":{"self":[{"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/posts\/5716","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/comments?post=5716"}],"version-history":[{"count":13,"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/posts\/5716\/revisions"}],"predecessor-version":[{"id":5730,"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/posts\/5716\/revisions\/5730"}],"wp:attachment":[{"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/media?parent=5716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/categories?post=5716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/experimentalmath.info\/blog\/wp-json\/wp\/v2\/tags?post=5716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}