A refinement of an estimate of the arithmetic minimum of the product of nonhomogeneous linear forms (regarding Minkowski's nonhomogeneous conjecture)

One refines an estimate of B. F. Skubenko (Tr. Mat. Inst. Akad. Nauk 148, 218–224 (1978)). Let be a point lattice of determinant d() in the n-dimensional Euclidean space ⁿ. and let L^ñ. We consider the nonhomogeneous One proves that there exists an effectively computable constant n_o such that if nn_o, then.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 82, pp. 88–94, 1979.