CONVERGENCE OF MADELUNG LIKE LATTICE SUM

➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạm

Loại tài liệu: PDF

Số trang: 46 Trang

Tài liệu: ✅ ĐÃ ĐƯỢC PHÊ DUYỆT

TẢI VỀ

Nội dung chi tiết: CONVERGENCE OF MADELUNG LIKE LATTICE SUM

CONVERGENCE OF MADELUNG LIKE LATTICE SUM

Convergence of Madelung-Like Lattice SumsDavid Borwei.n’ .Iona I HAN M. Bokwein* Christopher Pinner5June, 1993Abstracttt'r make a general study of the

CONVERGENCE OF MADELUNG LIKE LATTICE SUM e convergence properties of lattice sums, involving potentials, of the form occuring in Mathematical Chemistry and Physics Many specific examples are

studied in detail The prototype is Madelung's constant for NaCI:‘/ Jj. + m+n>7 -.^...=z - -1.Ĩ47ÕG45!)“ ựrp + m1 + />-■presuming that one appropriatel CONVERGENCE OF MADELUNG LIKE LATTICE SUM

y interprets the summation proceeds.Keywords: lattice sums, zeta functions, conditional convergence. Madelung's con-stant. Dirichlet series, theta fun

CONVERGENCE OF MADELUNG LIKE LATTICE SUM

ctions.AMS (1991) subject classification Primary 111’21. 40A05; Secondary 11S4ÍI. 4DIỈÍ15. A2D25. 30B50.* Department of Mathematics, rDiversity of Wes

Convergence of Madelung-Like Lattice SumsDavid Borwei.n’ .Iona I HAN M. Bokwein* Christopher Pinner5June, 1993Abstracttt'r make a general study of the

CONVERGENCE OF MADELUNG LIKE LATTICE SUM . Simon Erase* Univwrsity, Burn aby. BC V.'>A ISfi. Canada; jborseinicects.8ÍU.ca (Research supported by the Shrum Endowment ar Simon barer CnivetMly

and NSE.RC.)^Centre for Experimental and Constructive Mathematics. Simon Eraser University. Burn aby, BC V5A ISO, Canada & Depart.....nt of Matliruiat CONVERGENCE OF MADELUNG LIKE LATTICE SUM

io, I'nivi-rsity of British Columbia,Vancouver. HC VfiT 1Z2. Canada: pinncrCccca.siu.ca.12Bohwux. Botnvux ANI> PinNKR1IntroductionLattice sums of the

CONVERGENCE OF MADELUNG LIKE LATTICE SUM

form arising ill crystalline structures ami defined precisely ill the next section have been subject to intrusive study. A very good overview is avail

Convergence of Madelung-Like Lattice SumsDavid Borwei.n’ .Iona I HAN M. Bokwein* Christopher Pinner5June, 1993Abstracttt'r make a general study of the

CONVERGENCE OF MADELUNG LIKE LATTICE SUM to interpret their convergence is discussed ill |2. 1. 3. I| and the references therein. The prototype is Madelung ’.s constant for .Vat'l:- (-nn+m+p)

.= -1.71756159-- -X. V »’ ++ /' ■*presuming that one sums over expanding cubes but not spheres. [1].Sime the analytic or numerical evaluations of such CONVERGENCE OF MADELUNG LIKE LATTICE SUM

sums usually proceed by transform (ami "renormalization") -methods, these issues are often obscured especially in the physical science literature. As

CONVERGENCE OF MADELUNG LIKE LATTICE SUM

we shall illustrate ill this paper, while some general theorems arc available, the precise study of convergence is a delicate ami varied subject. Som

Convergence of Madelung-Like Lattice SumsDavid Borwei.n’ .Iona I HAN M. Bokwein* Christopher Pinner5June, 1993Abstracttt'r make a general study of the

CONVERGENCE OF MADELUNG LIKE LATTICE SUM [.ri...J*]t—I >=Iis a positive definite quadratic form with

ie the set of(«i.«t) fz R‘such that (ui/rz..... r/fr/tz) € c ami setGf := rfn|Z*\(()...())).We shall chiefly be interested in c c R‘ where {().II) lie CONVERGENCE OF MADELUNG LIKE LATTICE SUM

s in the interior ofc so thatImi vC = R*.

Convergence of Madelung-Like Lattice SumsDavid Borwei.n’ .Iona I HAN M. Bokwein* Christopher Pinner5June, 1993Abstracttt'r make a general study of the