## 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.

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.

Original language | English |
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Journal | Rendiconti Lincei Matematica e Applicazioni |

Publication status | Published - 2021 |