Algebraic independence for values of integral curves

Author: 

Fonseca, T

Publication Date: 

23 March 2019

Journal: 

Algebra and Number Theory

Last Updated: 

2020-08-26T05:23:35.14+01:00

Issue: 

3

Volume: 

13

DOI: 

10.2140/ant.2019.13.643

page: 

643-694

abstract: 

We prove a transcendence theorem concerning values of holomorphic maps from a disk to a quasi-projective variety over Q that are integral curves of some algebraic vector field (defined over Q). 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 E2, E4, E6. 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.

Symplectic id: 

963704

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article