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Czasopismo

1994 | 68 | 4 | 383-393

Tytuł artykułu

Mean square limit for lattice points in a sphere

Treść / Zawartość

Języki publikacji

EN

Czasopismo

Rocznik

Tom

68

Numer

4

Strony

383-393

Daty

wydano
1994
otrzymano
1994-03-12
poprawiono
1994-04-25

Twórcy

  • Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 Blackford Street, Indianapolis, Indiana 46202-3272 U.S.A.
  • School of Natural Sciences, Institute For Advanced Study, Princeton, New Jersey 08540, U.S.A.

Bibliografia

  • [AP] S. D. Adhikari and Y.-F. S. Pétermann, Lattice points in ellipsoids, Acta Arith. 59 (1991), 329-338.
  • [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.
  • [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.
  • [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.
  • [BK] M. N. Bleicher and M. I. Knopp, Lattice points in a sphere, Acta Arith. 10 (1965), 369-376.
  • [CI] F. Chamizo and H. Iwaniec, A 3-dimensional lattice point problem, in preparation.
  • [CN] K. Chandrasekharan and R. Narasimhan, Hecke's functional equation and the average order of arithmetical functions, Acta Arith. 6 (1961), 487-503.
  • [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.
  • [Cra] H. Cramér, Über zwei Sätze von Herrn G. H. Hardy, Math. Z. 15 (1922), 201-210.
  • [Gro] E. Grosswald, Representations of Integers as Sums of Squares, Springer, New York, 1985.
  • [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.
  • [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.
  • [KN] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies, II, Acta Arith. 62 (1992), 285-295.
  • [Lan1] E. Landau, Vorlesungen über Zahlentheorie, V. 1, Hirzel, Leipzig, 1927.
  • [Lan2] E. Landau, Ausgewählte Abhandlungen zur Gitterpunktlehre, A. Walfisz (ed.), Deutscher Verlag der Wiss., Berlin, 1962.
  • [Now] W. G. Nowak, On the lattice rest of a convex body in $ℝ^s$, II, Arch. Math. (Basel) 47 (1986), 232-237.
  • [Ran] B. Randol, A lattice point problem, I, II, Trans. Amer. Math. Soc. 121 (1966), 257-268; 125 (1966), 101-113.
  • [Sze] G. Szegö, Beiträge zur Theorie der Laguerreschen Polynome. II: Zahlentheoretische Anwendungen, Math. Z. 25 (1926), 388-404.
  • [Vau] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge University Press, Cambridge, 1981.
  • [Vin1] I. M. Vinogradov, On the number of integral points in a given domain, Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960), 777-786.
  • [Vin2] I. M. Vinogradov, On the number of integral points in a sphere, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 957-968.
  • [Wal] A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln, PWN, Warszawa, 1957.

Identyfikator YADDA

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