Rational values of Weierstrass zeta functions

G. O. Jones, M. E M Thomas

    Research output: Contribution to journalArticlepeer-review


    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(logT)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.

    Original languageEnglish
    Pages (from-to)1-14
    Number of pages14
    JournalProceedings of the Edinburgh Mathematical Society
    Publication statusAccepted/In press - 22 Dec 2015


    • counting
    • irrationality
    • Weierstrass zeta functions


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