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.
@article{119360,
author = {Ekkehard Kr\"atzel},
title = {Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {755-771},
zbl = {1064.11064},
mrnumber = {2046193},
language = {en},
url = {http://dml.mathdoc.fr/item/119360}
}
Krätzel, Ekkehard. Lattice points in some special three-dimensional convex bodies with points of Gaussian curvature zero at the boundary. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 755-771. http://gdmltest.u-ga.fr/item/119360/
Asymptotic Expansions, At the University Press, Cambridge, 1965. | MR 0168979 | Zbl 1096.41001
Area, Lattice Points and Exponential Sums, Clarendon Press, Oxford, 1996. | MR 1420620 | Zbl 0861.11002
Lattice Points, Dt. Verlag d. Wiss., Berlin and Kluwer Academic Publishers, Dordrecht/Boston/London, 1988. | MR 0998378
Double exponential sums, Analysis 16 (1996), 109-123. (1996) | MR 1397574
Lattice points in super spheres, Comment. Math. Univ. Carolinae 40.2 (1999), 373-391. (1999) | MR 1732659
Analytische Funktionen in der Zahlentheorie, B.G. Teubner, Stuttgart-Leipzig-Wiesbaden, 2000. | MR 1889901
Lattice points in three-dimensional convex bodies with points of Gaussian curvature zero at the boundary, Monatsh. Math., 2001. | MR 1942619
On sums of two k-th powers of numbers in residue classes II., Abh. Math. Sem. Univ. Hamburg 63 (1993), 87-95. (1993) | MR 1227866 | Zbl 0799.11037