## Abstract

We answer a question of Masser by showing that for the Weierstrass zeta function ζ corresponding to a given lattice Λ, the density of algebraic points of absolute multiplicative height bounded by T and degree bounded by k lying on the graph of ζ, restricted to an appropriate domain, does not exceed c(logT)^{15} for an effective constant c > 0 depending on k and on Λ. Using different methods, we also give two bounds of the same form for the density of algebraic points of bounded height in a fixed number field lying on the graph of ζ restricted to an appropriate subset of (0, 1). In one case the constant c can be shown not to depend on the choice of lattice; in the other, the exponent can be improved to 12.

Original language | English |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Proceedings of the Edinburgh Mathematical Society |

DOIs | |

Publication status | Accepted/In press - 22 Dec 2015 |

## Keywords

- counting
- irrationality
- Weierstrass zeta functions