Rational values of Weierstrass zeta functions

2016
Jones, Gareth O.
Journal article
Published in
Proceedings of the Edinburgh Mathematical Society (PEMS) ; 59 (2016), 4. - pp. 945-958. - ISSN 0013-0915. - eISSN 1464-3839
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(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.
510 Mathematics
Keywords
Weierstrass zeta functions, counting, irrationality
Cite This
ISO 690JONES, Gareth O., Margaret E. M. 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
BibTex
@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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Yes