# Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary

Commentationes Mathematicae Universitatis Carolinae (2002)

- Volume: 43, Issue: 4, page 755-771
- ISSN: 0010-2628

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topKrätzel, Ekkehard. "Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary." Commentationes Mathematicae Universitatis Carolinae 43.4 (2002): 755-771. <http://eudml.org/doc/248961>.

@article{Krätzel2002,

abstract = {We investigate the number of lattice points in special three-dimensional convex bodies. They are called convex bodies of pseudo revolution, because we have in one special case a body of revolution and in another case even a super sphere. These bodies have lines at the boundary, where all points have Gaussian curvature zero. We consider the influence of these points to the lattice rest in the asymptotic representation of the number of lattice points.},

author = {Krätzel, Ekkehard},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {convex bodies; lattice points; points with Gaussian curvature zero; body of revolution; Gaussian curvature; super sphere; lattice points},

language = {eng},

number = {4},

pages = {755-771},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary},

url = {http://eudml.org/doc/248961},

volume = {43},

year = {2002},

}

TY - JOUR

AU - Krätzel, Ekkehard

TI - Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2002

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 43

IS - 4

SP - 755

EP - 771

AB - We investigate the number of lattice points in special three-dimensional convex bodies. They are called convex bodies of pseudo revolution, because we have in one special case a body of revolution and in another case even a super sphere. These bodies have lines at the boundary, where all points have Gaussian curvature zero. We consider the influence of these points to the lattice rest in the asymptotic representation of the number of lattice points.

LA - eng

KW - convex bodies; lattice points; points with Gaussian curvature zero; body of revolution; Gaussian curvature; super sphere; lattice points

UR - http://eudml.org/doc/248961

ER -

## References

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- Krätzel E., Lattice Points, Dt. Verlag d. Wiss., Berlin and Kluwer Academic Publishers, Dordrecht/Boston/London, 1988. MR0998378
- Krätzel E., Double exponential sums, Analysis 16 (1996), 109-123. (1996) MR1397574
- Krätzel E., Lattice points in super spheres, Comment. Math. Univ. Carolinae 40.2 (1999), 373-391. (1999) MR1732659
- Krätzel E., Analytische Funktionen in der Zahlentheorie, B.G. Teubner, Stuttgart-Leipzig-Wiesbaden, 2000. MR1889901
- Krätzel E., Lattice points in three-dimensional convex bodies with points of Gaussian curvature zero at the boundary, Monatsh. Math., 2001. MR1942619
- Kuba G., On sums of two k-th powers of numbers in residue classes II., Abh. Math. Sem. Univ. Hamburg 63 (1993), 87-95. (1993) Zbl0799.11037MR1227866

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