On algebraic values of Weierstrass σ-functions

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Abstract

Suppose that
is a lattice in the complex plane and let be the corresponding
Weierstrass -function. Assume that the point associated with
in the standard fundamental
domain has imaginary part at most 1.9. Assuming that
has algebraic invariants g2; g3 we
show that a bound of the form cdm(logH)n holds for the number of algebraic points of height
at most H and degree at most d lying on the graph of . To prove this we apply results by
Masser and Besson. What is perhaps surprising is that we are able to establish such a bound
for the whole graph, rather than some restriction. We prove a similar result when, instead of
g2; g3, the lattice points are algebraic. For this we naturally exclude those (z; (z)) for which z 2.

Bibliographical metadata

Original languageEnglish
JournalRendiconti Lincei Matematica e Applicazioni
Publication statusPublished - 2021