Abstract
One obtains the following transfer theorem, related to Minkowski's nonhomogeneous conjecture. Let Λ ⊂ ℝn be a point lattice, det Λ=1. We consider the nonhomogeneous Π(Λ) and the homogeneous L(Λ)=бn. б ⩾ 0, arithmetical minima of the lattice Λ. Then for sufficiently largen, if
, then
.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
K. B. Bakiev, A. S. Pen, and B. F. Skubenko, “On an upper bound for the product of linear nonhomogeneous forms,” Mat. Zametki,23, No. 6, 789–796 (1978).
B. F. Skubenko, “Minkowski's conjecture for large n,” Tr. Mat. Inst. Akad. Nauk SSSR,148, 218–224 (1978).
B. F. Skubenko and K. B. Bakiev, “The transfer theorem in the nonhomogeneous Minkowski problem,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,91, 119–124 (1979).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 106, pp. 5–16, 1981.
Rights and permissions
About this article
Cite this article
Bakiev, K.B. An upper estimate for the product linear nonhomogeneous forms for lattices with a small homogeneous minimum. J Math Sci 23, 2107–2114 (1983). https://doi.org/10.1007/BF01566950
Issue Date:
DOI: https://doi.org/10.1007/BF01566950