An Ω + -estimate for the number of lattice points in a sphere

Werner Georg Nowak

Rendiconti del Seminario Matematico della Università di Padova (1985)

  • Volume: 73, page 31-40
  • ISSN: 0041-8994

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Nowak, Werner Georg. "An $\Omega _+$-estimate for the number of lattice points in a sphere." Rendiconti del Seminario Matematico della Università di Padova 73 (1985): 31-40. <http://eudml.org/doc/107986>.

@article{Nowak1985,
author = {Nowak, Werner Georg},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {omega-estimate; number of lattice points in sphere; lattice remainder; sum of three squares},
language = {eng},
pages = {31-40},
publisher = {Seminario Matematico of the University of Padua},
title = {An $\Omega _+$-estimate for the number of lattice points in a sphere},
url = {http://eudml.org/doc/107986},
volume = {73},
year = {1985},
}

TY - JOUR
AU - Nowak, Werner Georg
TI - An $\Omega _+$-estimate for the number of lattice points in a sphere
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1985
PB - Seminario Matematico of the University of Padua
VL - 73
SP - 31
EP - 40
LA - eng
KW - omega-estimate; number of lattice points in sphere; lattice remainder; sum of three squares
UR - http://eudml.org/doc/107986
ER -

References

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  2. [2] B.C. Berndt, On the average order of a class of arithmetical functions I, II, J. Number Theory, 3 (1971), pp. 184-203 and 288-305. Zbl0219.10050MR284409
  3. [3] K. Chandrasekharan - R. Narasimhan, Hecke's functional equation and the average order of arithmetical functions, Acta Arith., 6 (1961), pp. 487-503. Zbl0101.03703MR126423
  4. [4] J.R. Chen, The lattice points in a circle, Chin. Math., 4 (1963), pp. 322-339. Zbl0147.03302MR184912
  5. [5] K. Corrádi - I. Kátai, A comment on K. S. Gangadharan's paper entitled « Two classical lattice point problems» (in Hungarian), Magyar. Tud. Akad. Mat. Fiz. Oszt. Közl., 17 (1967), pp. 89-97. Zbl0163.04103MR215800
  6. [6] F. Fricker, Einführung in die Gitterpunktlehre, Basel, Boston, Suttgart: Birkhäuser, 1982. Zbl0489.10001MR673938
  7. [7] K.S. Gangadharan, Two classical lattice point problems, Proc. Cambridge, 57 (1961), pp. 699-721. Zbl0100.03901MR130225
  8. [8] J.L. Hafner, On the average order of a class of arithmetical functions, J. Number Theory, 15 (1982), pp. 36-76. Zbl0495.10027MR666348
  9. [9] G.H. Hardy, On the expression of a number as the sum of two squares, Quart. J. Math., 46 (1915), pp. 263-283. Zbl45.1253.01JFM45.1253.01
  10. [10] S. Kanemitsu, Some results in the divisor problems, to appear. Zbl1294.05091
  11. [11] E. Landau, Elementary number theory, 2nd ed., New York, Chelsea Publ. Co., 1955. Zbl0079.06201MR92794
  12. [12] D. Redmond, Omega theorems for a class of Dirichlet series, Rocky Mt. J. Math., 9 (1979), pp. 733-748. Zbl0388.10027MR560250
  13. [13] G. Szegö, Beiträge zur Theorie der Laguerreschen Polynome, II: Zahlentheoretische Anwendungen, Math. Z., 25 (1926), pp. 388-404. Zbl52.0175.03MR1544819JFM52.0175.03
  14. [14] 1 M. Vinogradov, On the number of lattice points in a sphere (in Russian), Izv. Akad. Nauk. SSSR Ser. Mat., 27 (1963), pp. 957-968. Zbl0116.03901MR156821
  15. [15] I.M. Vinogradov, Special variants of the method of trigonometric sums (in Russian), Moscow, Nauka, 1976. Zbl0429.10023MR469878

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