Multiplicity estimates for analytic functions II

Lower bounds for zero-dimensional projections

“…This result in turn will follow, using an improvement of Lemma 5 of [4], from the following result: Theorem 3. Let the homogeneous prime ideal P ⊂ A have dimension d. Let the homogeneous polynomials b P1, .…”

Fields of large transcendence degree generated by values of elliptic functions

“…In this chapter we give a general estimate, that seems to be not quite well-known, for primary components of a homogeneous ideal 3 of 9t. While the result is more or less implicit in the arguments of [4] (section 5), it seems clearer to give an explicit statement for future applications. Recall that a non-zero proper homogeneous ideal 3 of ~R has rank r satisfying 1 <_ r < n + 1.…”

“…In the inductive construction of the next section we shall make frequent use of a standard argument from [4] and [17]. Thus it is convenient to formulate it here in a general context.…”

Simultaneous approximation of et and ℘(t)

“…REMARK 3. By using the above method (see [1] for more details) many other numbers involving values of the elliptic function can be approximated simultaneously. As an example, we can deal with algebraic points of an elliptic function.…”