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# Rational values of Weierstrass zeta functions

Type of Publication: | Journal article |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-284194 |

Author: | Jones, Gareth O.; Thomas, Margaret |

Year of publication: | 2016 |

Published in: | Proceedings of the Edinburgh Mathematical Society (PEMS) ; 59 (2016), 4. - pp. 945-958. - ISSN 0013-0915. - eISSN 1464-3839 |

DOI (citable link): | https://dx.doi.org/10.1017/S0013091515000309 |

Summary: |
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)
^{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. |

Subject (DDC): | 510 Mathematics |

Keywords: | Weierstrass zeta functions, counting, irrationality |

Link to License: | In Copyright |

Bibliography of Konstanz: | Yes |

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Checksum:
MD5:1b5cbfc07ef04499e8775e84c997eecd

JONES, Gareth O., Margaret THOMAS, 2016. Rational values of Weierstrass zeta functions. In: Proceedings of the Edinburgh Mathematical Society (PEMS). 59(4), pp. 945-958. ISSN 0013-0915. eISSN 1464-3839. Available under: doi: 10.1017/S0013091515000309

@article{Jones2016Ratio-30336, title={Rational values of Weierstrass zeta functions}, year={2016}, doi={10.1017/S0013091515000309}, 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} }

Jones_0-284194.pdf | 198 |