The PI will investigate several different, yet mutually connected problems in number theory. One part will focus on the asymptotic behavior of integral solutions to inhomogeneous Pell inequalities. Another part of this proposal deals with the study of the global version to the part just described, namely, counting the number of lattice points in tilted rectangles. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.
