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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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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} }

2016 Jones, Gareth O. 2015-03-17T12:25:19Z Rational values of Weierstrass zeta functions eng terms-of-use Thomas, Margaret 2015-03-17T12:25:19Z 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)<sup>15</sup>, 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. Jones, Gareth O. Thomas, Margaret

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