Vol. 13, No. 3, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Algebraic independence for values of integral curves

Tiago J. Fonseca

Vol. 13 (2019), No. 3, 643–694

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 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.

algebraic independence, transcendence, integral curves, modular forms, Eisenstein series, differential equations, Nevanlinna theory, integrality, zero lemma
Mathematical Subject Classification 2010
Primary: 11J81
Secondary: 14G40, 37F75, 32A22
Received: 17 May 2018
Accepted: 25 December 2018
Published: 23 March 2019
Tiago J. Fonseca
Mathematical Institute
University of Oxford
United Kingdom