Abstract
We prove a transcendence theorem concerning values of holomorphic maps from a disk to a quasiprojective variety over that are integral curves of some algebraic vector field (defined over ). These maps are required to satisfy some integrality property, besides a growth condition and a strong form of Zariski-density that are natural for integral curves of algebraic vector fields.
This result generalizes a theorem of Nesterenko concerning algebraic independence of values of the Eisenstein series , , . The main technical improvement in our approach is the replacement of a rather restrictive hypothesis of polynomial growth on Taylor coefficients by a geometric notion of moderate growth formulated in terms of value distribution theory.
Citation
Tiago J. Fonseca. "Algebraic independence for values of integral curves." Algebra Number Theory 13 (3) 643 - 694, 2019. https://doi.org/10.2140/ant.2019.13.643
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