On the number of lattice points in thin sectors (Q6565887)

In an extension of the classical problem of determining the number of lattice points inside a circle of radius \(R\), the authors study the number of lattice points in a sector with edges given by \(y = (\alpha + \varepsilon)x\) where \(\varepsilon\) goes to \(0\) as \(R\) approaches infinity. They give an asymptotic count for the number of integer lattice points lying in this sector that depends on the decay rate of \(\varepsilon\) and on the rationality/irrationality type of \(\alpha\).