Asymptotics for minimal discrete energy on the sphere

Transactions of the American Mathematical Society

Volumn 350, Issue 2, 1998, Pages 523-538

  Kuijlaars, A B J ^a,b   Saff, E B ^c  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944444965     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-98-02119-9     Document Type: Article

References (24)

1. 1] J. Beck and W. Chen, Irregularities of distribution, Cambridge Univ. Press, Cambridge, 1987. MR 88m:11061
2. 2] A. A. Berezin, Asymptotics for thé maximum number of repulsive particles on a spherical surface, J. Math. Phys. 27 (1986), 1533-1536. MR 87j:31010
3. 3] B. Bergersen, D. Boal and P. Palffy-Muhoray, Equilibrium configurations of particles on a sphere: the case of logarithmic interactions, J. Phys. A: Math. Gen. 27 (1994), 2579-2586.
4. 4] H. F. Blichfeldt, A new principle in the geometry of numbers, with some applications, Trans. Amer. Math. Soc. 15 (1914), 227-235.
5. 5] D. Borwein, J. M. Borwein, R. Shail and I. J. Zucker, Energy of static electron lattices, J. Phys. A: Math. Gen. 21 (1988), 1519-1531. MR 89f:82070
6. 6] J. Bourgain and J. Lindenstrauss, Distribution of points on spheres and approximation by zonotopes, Israel J. Math. 64 (1988), 25-31. MR 90g:46021
7. 7] H. Cohn, Advanced Number Theory, Dover, New York, 1980. MR 82b: 12001
8. 8] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Springer-Verlag, New York, 1993. MR 93h:11069
9. 9] B. E. J. Dahlberg, On the distribution of Fekete points, Duke Math. J. 45 (1978), 537-542. MR 80c:31003
10. 10] T. Erber and G. M. Hockney, Equilibrium configurations of N equal charges on a sphere, J. Phys. A: Math. Gen. 24 (1991), L1369-L1377.
11. 11] L. Classer and A. G. Every, Energies and spacings of point charges on a sphere, J. Phys. A: Math. Gen. 25 (1992), 2473-2482.
12. 12] W. Habicht and B. L. van der Waerden, Lagerung von Punkten auf der Kugel, Math. Ann. 123 (1951), 223-234. MR 13:154d
13. 13] E. Landau, Ausgewählte Abhandlungen zur Gitterpunktlehre, VEB Deutscher Verlag der Wissenschaften, Berlin, 1962. MR 27:112
14. 14] N. S. Landkof, Foundations of Modern Potential Theory, Grundl. math. Wiss. vol. 180, Springer-Verlag, Berlin, 1972. MR 50:2520
15. 15] T. W. Melnyk, O. Knop and W. R. Smith, Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited, Can. J. Chem. 55 (1977), 1745-1761. MR 56:2848
16. 16] C. Müller, Spherical Harmonics, Lect. Notes. Math. 17, Springer-Verlag, Berlin, 1966. MR 33:7593
17. 17] E. A. Rakhmanov, E. B. Saff and Y. M. Zhou, Minimal discrete energy on the sphere, Mathematical Research Letters 1 (1994), 647-662. MR 96e:78011
18. 18] E. A. Rakhmanov, E. B. Saff and Y. M. Zhou, Electrons on the sphere, In: Computational Methods and Function Theory (R.M. All, St. Ruscheweyh and E.B. Saff, Eds.), World Scientific, 1995, pp. 111-127. MR 97h:78013
19. 19] I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96-108. MR 3:232c
20. 20] M. Shub and S. Smale, Complexity of Bezout's theorem III: Condition number and packing, J. Complexity 9 (1993), 4-14. MR 94g:65152
21. 21] G. Szegö, Orthogonal Polynomials, Amer. Math. Soc., Providence RI, 1967. MR 46:9631
22. 22] B. L. van der Waerden, Punkte auf der Kugel, drei Zusätze, Math. Ann. 125 (1952), 213-222. MR 14:401c
23. 23] G. Wagner, On the means of distances on the surface of a sphere (lower bounds), Pacific J. Math. 144 (1990), 389-398. MR 91e:52014
24. 24] G. Wagner, On the means of distances on the surface of a sphere II (upper bounds), Pacific J. Math. 153 (1992), 381-396. MR 93b:52007