Convergence of Madelung-like lattice sums

被引：15

作者：

Borwein, D ^{[1
]}

Borwein, JM

Pinner, C

机构：

[1] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada

[2] Simon Fraser Univ, Ctr Expt & Construct Math, Burnaby, BC V5A 1S6, Canada

[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 350卷 / 08期

关键词：

lattice sums; zeta functions; conditional convergence; Madelung's constant; Dirichlet series; theta functions;

D O I：

10.1090/S0002-9947-98-01983-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We make a general study of the convergence properties of lattice sums, involving potentials, of the form occurring in mathematical chemistry and physics. Many specific examples are studied in detail. The prototype is Madelung's constant for NaCl: [GRAPHICS] presuming that one appropriately interprets the summation proccess.

引用

页码：3131 / 3167

页数：37

共 22 条

[1]

[Anonymous], THEORETICAL CHEM ADV

[2] ANALYSIS OF CERTAIN LATTICE SUMS [J].

BORWEIN, D ;

BORWEIN, JM ;

SHAIL, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 143 (01) :126-137

[3] CONVERGENCE OF LATTICE SUMS AND MADELUNG CONSTANT [J].

BORWEIN, D ;

BORWEIN, JM ;

TAYLOR, KF .

JOURNAL OF MATHEMATICAL PHYSICS, 1985, 26 (11) :2999-3009

[4]

BORWEIN JM, 1908, PI AGM STUDY ANAL NU

[5] ON THE CONVERGENCE PROBLEM FOR LATTICE SUMS [J].

BUHLER, JP ;

CRANDALL, RE .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (12) :2523-2528

[6]

Hardy G. H., 1915, CAMBRIDGE TRACTS MAT, V18

[7]

HUXLEY MN, 1993, P LOND MATH SOC, V66, P279

[8] REMARKS ON A LATTICE POINT PROBLEM [J].

KRATZEL, E .

MATHEMATISCHE ANNALEN, 1969, 179 (02) :90-&

[9]

KRATZEL E, 1992, ACTA ARITH, V62, P285

[10]

Landau E, 1915, SITZBER K PREUSS AKA, P458

← 1 2 3 →