On the average order of the lattice rest of a convex body

Wolfgang Müller

Acta Arithmetica (1997)

  • Volume: 80, Issue: 1, page 89-100
  • ISSN: 0065-1036

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Wolfgang Müller. "On the average order of the lattice rest of a convex body." Acta Arithmetica 80.1 (1997): 89-100. <http://eudml.org/doc/207030>.

@article{WolfgangMüller1997,
author = {Wolfgang Müller},
journal = {Acta Arithmetica},
keywords = {lattice points; average order; convex body; number of lattice points; blown up domain; lattice rest},
language = {eng},
number = {1},
pages = {89-100},
title = {On the average order of the lattice rest of a convex body},
url = {http://eudml.org/doc/207030},
volume = {80},
year = {1997},
}

TY - JOUR
AU - Wolfgang Müller
TI - On the average order of the lattice rest of a convex body
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 1
SP - 89
EP - 100
LA - eng
KW - lattice points; average order; convex body; number of lattice points; blown up domain; lattice rest
UR - http://eudml.org/doc/207030
ER -

References

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  1. [1] R. N. Bhattacharya and R. R. Rao, Normal Approximation and Asymptotic Expansions, Wiley, New York, 1976. Zbl0331.41023
  2. [2] S. Bochner, Die Poissonsche Summenformel in mehreren Veränderlichen, Math. Ann. 106 (1932), 55-63. Zbl58.0283.01
  3. [3] E. Hlawka, Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1-36. 
  4. [4] E. Hlawka, Über Integrale auf konvexen Körpern II, ibid., 81-99. 
  5. [5] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301. Zbl0820.11060
  6. [6] M. N. Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523-531. Zbl0845.11036
  7. [7] A. E. Ingham, A note on Fourier transforms, J. London Math. Soc. 9 (1934), 29-32. Zbl0008.30601
  8. [8] V. Jarník, Über Gitterpunkte in mehrdimensionalen Kugeln, Math. Ann. 100 (1928), 699-721. Zbl54.0203.01
  9. [9] V. Jarník, Über die Mittelwertsätze der Gitterpunktlehre, 5. Abhandlung, Časopis Pěst. Mat. 69 (1940), 148-174. Zbl0023.11202
  10. [10] I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60. Zbl0151.04401
  11. [11] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies, Monatsh. Math. 112 (1991), 61-72. Zbl0754.11027
  12. [12] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies II, Acta Arith. 62 (1992), 285-295. Zbl0769.11037
  13. [13] K. Leichtweiss, Konvexe Mengen, Springer, Berlin, 1980. 
  14. [14] W. G. Nowak, On the average order of the lattice rest of a convex planar domain, Proc. Cambridge Philos. Soc. 98 (1985), 1-4. Zbl0552.10032
  15. [15] W. G. Nowak, An Ω-estimate for the lattice rest of a convex planar domain, Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 295-299. Zbl0582.10033
  16. [16] W. G. Nowak, On the lattice rest of a convex body in ℝ s , Arch. Math. (Basel) 45 (1985), 284-288. Zbl0552.10033
  17. [17] W. G. Nowak, On the lattice rest of a convex body in ℝ s , II, ibid. 47 (1986), 232-237. 
  18. [18] W. G. Nowak, On the lattice rest of a convex body in ℝ s , III, Czechoslovak Math. J. 41 (116) (1991), 359-367. Zbl0745.11044
  19. [19] J. A. Thorpe, Elementary Topics in Differential Geometry, Springer, New York, 1979. Zbl0404.53001
  20. [20] A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln, Monografie Mat. 33, Polish Scientific Publ., Warszawa, 1957. 

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