On the average order of the lattice rest of a convex body
Wolfgang Müller
Acta Arithmetica, Tome 80 (1997), p. 89-100 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1997-01-01
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     author = {Wolfgang M\"uller},
     title = {On the average order of the lattice rest of a convex body},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {89-100},
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     language = {en},
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Wolfgang Müller. On the average order of the lattice rest of a convex body. Acta Arithmetica, Tome 80 (1997) pp. 89-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav80i1p89bwm/

[000] [1] R. N. Bhattacharya and R. R. Rao, Normal Approximation and Asymptotic Expansions, Wiley, New York, 1976. | Zbl 0331.41023

[001] [2] S. Bochner, Die Poissonsche Summenformel in mehreren Veränderlichen, Math. Ann. 106 (1932), 55-63. | Zbl 58.0283.01

[002] [3] E. Hlawka, Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1-36.

[003] [4] E. Hlawka, Über Integrale auf konvexen Körpern II, ibid., 81-99.

[004] [5] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301. | Zbl 0820.11060

[005] [6] M. N. Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523-531. | Zbl 0845.11036

[006] [7] A. E. Ingham, A note on Fourier transforms, J. London Math. Soc. 9 (1934), 29-32. | Zbl 0008.30601

[007] [8] V. Jarník, Über Gitterpunkte in mehrdimensionalen Kugeln, Math. Ann. 100 (1928), 699-721. | Zbl 54.0203.01

[008] [9] V. Jarník, Über die Mittelwertsätze der Gitterpunktlehre, 5. Abhandlung, Časopis Pěst. Mat. 69 (1940), 148-174. | Zbl 0023.11202

[009] [10] I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60. | Zbl 0151.04401

[010] [11] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies, Monatsh. Math. 112 (1991), 61-72. | Zbl 0754.11027

[011] [12] E. Krätzel and W. G. Nowak, Lattice points in large convex bodies II, Acta Arith. 62 (1992), 285-295. | Zbl 0769.11037

[012] [13] K. Leichtweiss, Konvexe Mengen, Springer, Berlin, 1980.

[013] [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. | Zbl 0552.10032

[014] [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. | Zbl 0582.10033

[015] [16] W. G. Nowak, On the lattice rest of a convex body in ℝs, Arch. Math. (Basel) 45 (1985), 284-288. | Zbl 0552.10033

[016] [17] W. G. Nowak, On the lattice rest of a convex body in ℝs, II, ibid. 47 (1986), 232-237.

[017] [18] W. G. Nowak, On the lattice rest of a convex body in ℝs, III, Czechoslovak Math. J. 41 (116) (1991), 359-367. | Zbl 0745.11044

[018] [19] J. A. Thorpe, Elementary Topics in Differential Geometry, Springer, New York, 1979. | Zbl 0404.53001

[019] [20] A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln, Monografie Mat. 33, Polish Scientific Publ., Warszawa, 1957.