The number of solutions of bounded height to a system of linear equations
The author considers the number of solutions with height \(\leq B\) of systems of homogeneous or inhomogeneous linear equations over a number field. Explicit asymptotic estimates with error terms are given for the number of such solutions as \(B\to\infty\). The constants involved in the formulas depend on the parameters of the number field. Similar results are obtained for the number of lattice points in certain bounded domains.
explicit asymptotic estimates with error terms
scientific article; zbMATH DE number 166072