Publikation: Rational values of Weierstrass zeta functions
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2016
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Jones, Gareth O.
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Proceedings of the Edinburgh Mathematical Society (PEMS). 2016, 59(4), pp. 945-958. ISSN 0013-0915. eISSN 1464-3839. Available under: doi: 10.1017/S0013091515000309
Zusammenfassung
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.
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Fachgebiet (DDC)
510 Mathematik
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Weierstrass zeta functions, counting, irrationality
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JONES, Gareth O., Margaret E. M. THOMAS, 2016. Rational values of Weierstrass zeta functions. In: Proceedings of the Edinburgh Mathematical Society (PEMS). 2016, 59(4), pp. 945-958. ISSN 0013-0915. eISSN 1464-3839. Available under: doi: 10.1017/S0013091515000309BibTex
@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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<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)<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.</dcterms:abstract>
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