Sums of multiplicative functions over a Beatty sequence

We study sums involving multiplicative functions that take values over a nonhomogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas for quantities such as the number of integers in a Beatty sequence that are representable as a sum of two squares up to a given magnitude. © 2008 Australian Mathematical Society

The Additive Ordered Structure of Natural Numbers with a Beatty Sequence

We have provided a pure model-theoretic proof for the decidability of the additive structure of the natural numbers together with a function {f} sending {x} to {[\phi x]} with {\phi} the golden ratio.Comment: 14 page