@article{Jones2016Ratio-30336,
  year={2016},
  doi={10.1017/S0013091515000309},
  title={Rational values of Weierstrass zeta functions},
  number={4},
  volume={59},
  issn={0013-0915},
  journal={Proceedings of the Edinburgh Mathematical Society (PEMS)},
  pages={945--958},
  author={Jones, Gareth O. and Thomas, Margaret E. M.}
}

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    <dc:creator>Thomas, Margaret E. M.</dc:creator>
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    <dcterms:abstract xml:lang="eng">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(log T)&lt;sup&gt;15&lt;/sup&gt;, for an effective constant c &gt; 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.</dcterms:abstract>
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    <dc:creator>Jones, Gareth O.</dc:creator>
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