Rational values of Weierstrass zeta functions

Jones, Gareth O.; Thomas, Margaret E. M.

Rational values of Weierstrass zeta functions

Dateien

Jones_0-284194.pdf(175.33 KB)

Datum

2016

Autor:innen

Jones, Gareth O.

Thomas, Margaret E. M.

Publikationstyp

Zeitschriftenartikel

Erschienen in

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

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Weierstrass zeta functions, counting, irrationality

Zitieren

ISO 690

JONES, 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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