Mean square limit for lattice points in a sphere

Pavel M. Bleher; Freeman J. Dyson

Acta Arithmetica (1994)

  • Volume: 68, Issue: 4, page 383-393
  • ISSN: 0065-1036

How to cite


Pavel M. Bleher, and Freeman J. Dyson. "Mean square limit for lattice points in a sphere." Acta Arithmetica 68.4 (1994): 383-393. <>.

author = {Pavel M. Bleher, Freeman J. Dyson},
journal = {Acta Arithmetica},
language = {eng},
number = {4},
pages = {383-393},
title = {Mean square limit for lattice points in a sphere},
url = {},
volume = {68},
year = {1994},

AU - Pavel M. Bleher
AU - Freeman J. Dyson
TI - Mean square limit for lattice points in a sphere
JO - Acta Arithmetica
PY - 1994
VL - 68
IS - 4
SP - 383
EP - 393
LA - eng
UR -
ER -


  1. [AP] S. D. Adhikari and Y.-F. S. Pétermann, Lattice points in ellipsoids, Acta Arith. 59 (1991), 329-338. Zbl0705.11056
  2. [Ble1] P. M. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math. J. 67 (1992), 461-481. Zbl0762.11031
  3. [Ble2] P. M. Bleher, Distribution of energy levels of a quantum free particle on a surface of revolution, Duke Math. J. 74 (1994), 45-93. 
  4. [BCDL] P. M. Bleher, Z. Cheng, F. J. Dyson and J. L. Lebowitz, Distribution of the error term for the number of lattice points inside a shifted circle, Comm. Math. Phys. 154 (1993), 433-469. Zbl0781.11038
  5. [BK] M. N. Bleicher and M. I. Knopp, Lattice points in a sphere, Acta Arith. 10 (1965), 369-376. Zbl0131.04701
  6. [CI] F. Chamizo and H. Iwaniec, A 3-dimensional lattice point problem, in preparation. 
  7. [CN] K. Chandrasekharan and R. Narasimhan, Hecke's functional equation and the average order of arithmetical functions, Acta Arith. 6 (1961), 487-503. Zbl0101.03703
  8. [Che] J.-R. Chen, Improvement on the asymptotic formulas for the number of lattice points in a region of the three dimensions (II), Sci. Sinica 12 (1963), 751-764. Zbl0127.27503
  9. [Cra] H. Cramér, Über zwei Sätze von Herrn G. H. Hardy, Math. Z. 15 (1922), 201-210. 
  10. [Gro] E. Grosswald, Representations of Integers as Sums of Squares, Springer, New York, 1985. Zbl0574.10045
  11. [HL] G. H. Hardy and J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet series whose coefficients are positive, Proc. London Math. Soc. 13 (1914), 174. Zbl45.0389.02
  12. [H-B] D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992), 389-415. Zbl0725.11045
  13. [KN] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies, II, Acta Arith. 62 (1992), 285-295. Zbl0769.11037
  14. [Lan1] E. Landau, Vorlesungen über Zahlentheorie, V. 1, Hirzel, Leipzig, 1927. 
  15. [Lan2] E. Landau, Ausgewählte Abhandlungen zur Gitterpunktlehre, A. Walfisz (ed.), Deutscher Verlag der Wiss., Berlin, 1962. 
  16. [Now] W. G. Nowak, On the lattice rest of a convex body in s , II, Arch. Math. (Basel) 47 (1986), 232-237. 
  17. [Ran] B. Randol, A lattice point problem, I, II, Trans. Amer. Math. Soc. 121 (1966), 257-268; 125 (1966), 101-113. 
  18. [Sze] G. Szegö, Beiträge zur Theorie der Laguerreschen Polynome. II: Zahlentheoretische Anwendungen, Math. Z. 25 (1926), 388-404. Zbl52.0175.03
  19. [Vau] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, Cambridge, 1981. 
  20. [Vin1] I. M. Vinogradov, On the number of integral points in a given domain, Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960), 777-786. 
  21. [Vin2] I. M. Vinogradov, On the number of integral points in a sphere, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 957-968. 
  22. [Wal] A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln, PWN, Warszawa, 1957. 

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