## Abstract

For a fixed b ∈ N = {1, 2, 3, . . .} we say that a point (r, s) in the integer lattice Z × Z is b-visible from the origin if it lies on the graph of a power function f(x) = ax^{b} with a and no other integer lattice point lies on this curve (i.e., line of sight) between (0, 0) and (r, s). We prove that the proportion of b-visible integer lattice points is given by 1/ζ(b + 1), where ζ(s) denotes the Riemann zeta function. We also show that even though the proportion of b-visible lattice points approaches 1 as b approaches infinity, there exist arbitrarily large rectangular arrays of b-invisible lattice points for any fixed b. This work specialized to b = 1 recovers original results from the classical lattice point visibility setting where the lines of sight are given by linear functions with rational slope through the origin.

Original language | English (US) |
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Pages (from-to) | 593-601 |

Number of pages | 9 |

Journal | American Mathematical Monthly |

Volume | 125 |

Issue number | 7 |

DOIs | |

State | Published - Aug 9 2018 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2018, © The Mathematical Association of America.

## Keywords

- Primary 11P21
- Secondary 11M99