Abstract:
An upper bound for the index of a sublattice, which arises in relation to various versions of zero lemmas in the theory of linear forms in logarithms of algebraic numbers, in terms of the Hilbert polynomial is found. Simultaneously, a lower bound for the values of this polynomial is obtained.
Keywords:algebraic number, logarithmic height, lattice, index of a sublattice, Hilbert polynomial, rational subspace.