Distributive and analytic properties of lattice sums

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dc.contributor.author McPhedran, RC
dc.contributor.author Smith, GH
dc.contributor.author Nicorovici, NA
dc.contributor.author Botten, LC
dc.date.accessioned 2009-12-21T02:28:00Z
dc.date.issued 2004-07
dc.identifier.citation Journal of Mathematical Physics, 2004, 45 (7), pp. 2560 - 2578
dc.identifier.issn 0022-2488
dc.identifier.other C1 en_US
dc.identifier.uri http://hdl.handle.net/10453/3420
dc.description.abstract We use sums over Bessel functions of the first kind to derive a convenient form of the Poisson summation identity relating sums over direct lattices in two dimensions to sums over reciprocal lattices. After three simple examples of the use of the identity, we consider sums over complex powers of the radial distance to lattice points, and also sums incorporating factors exp(4imψp) depending on angles of lattice points. We study the distribution of zeros of lattice sums, and show two which seemingly obey the Riemann hypothesis, and a third which does not. We provide a reflection formula for angular lattice sums, and a Macdonald function sum for the lowest order angular lattice sum. © 2004 American Institute of Physics.
dc.language eng
dc.relation.isbasedon 10.1063/1.1755861
dc.title Distributive and analytic properties of lattice sums
dc.type Journal Article
dc.description.version Published
dc.parent Journal of Mathematical Physics
dc.journal.volume 7
dc.journal.volume 45
dc.journal.number en_US
dc.publocation Melville en_US
dc.identifier.startpage 2560 en_US
dc.identifier.endpage 2578 en_US
dc.cauo.name SCI.Faculty of Science en_US
dc.conference Verified OK en_US
dc.for 0205 Optical Physics
dc.for 0105 Mathematical Physics
dc.personcode 701759
dc.personcode 780055
dc.personcode 950497
dc.percentage 50 en_US
dc.classification.name Mathematical Physics en_US
dc.classification.type FOR-08 en_US
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Science
utslib.copyright.status Closed Access
utslib.copyright.date 2015-04-15 12:17:09.805752+10
pubs.consider-herdc true
utslib.collection.history Uncategorised (ID: 363)
utslib.collection.history Closed (ID: 3)

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