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., 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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