Previous |  Up |  Next


convex bodies; lattice points; points with Gaussian curvature zero
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.
[1] Copson E.T.: Asymptotic Expansions. At the University Press, Cambridge, 1965. MR 0168979 | Zbl 1096.41001
[2] Huxley M.N.: Area, Lattice Points and Exponential Sums. Clarendon Press, Oxford, 1996. MR 1420620 | Zbl 0861.11002
[3] Krätzel E.: Lattice Points. Dt. Verlag d. Wiss., Berlin and Kluwer Academic Publishers, Dordrecht/Boston/London, 1988. MR 0998378
[4] Krätzel E.: Double exponential sums. Analysis 16 (1996), 109-123. MR 1397574
[5] Krätzel E.: Lattice points in super spheres. Comment. Math. Univ. Carolinae 40.2 (1999), 373-391. MR 1732659
[6] Krätzel E.: Analytische Funktionen in der Zahlentheorie. B.G. Teubner, Stuttgart-Leipzig-Wiesbaden, 2000. MR 1889901
[7] Krätzel E.: Lattice points in three-dimensional convex bodies with points of Gaussian curvature zero at the boundary. Monatsh. Math., 2001. MR 1942619
[8] Kuba G.: On sums of two k-th powers of numbers in residue classes II. Abh. Math. Sem. Univ. Hamburg 63 (1993), 87-95. MR 1227866 | Zbl 0799.11037
Partner of
EuDML logo