Algebraic independence for values of integral curves
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...
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| Định dạng: | Journal article |
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Mathematical Sciences Publishers
2019
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| _version_ | 1826283325126344704 |
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| author | Fonseca, T |
| author_facet | Fonseca, T |
| author_sort | Fonseca, T |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:57:13Z |
| format | Journal article |
| id | oxford-uuid:887d5d2f-2c20-41ff-86b1-008976da9992 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:57:13Z |
| publishDate | 2019 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:887d5d2f-2c20-41ff-86b1-008976da99922022-03-26T22:17:34ZAlgebraic independence for values of integral curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:887d5d2f-2c20-41ff-86b1-008976da9992Symplectic Elements at OxfordMathematical Sciences Publishers2019Fonseca, TWe 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. |
| spellingShingle | Fonseca, T Algebraic independence for values of integral curves |
| title | Algebraic independence for values of integral curves |
| title_full | Algebraic independence for values of integral curves |
| title_fullStr | Algebraic independence for values of integral curves |
| title_full_unstemmed | Algebraic independence for values of integral curves |
| title_short | Algebraic independence for values of integral curves |
| title_sort | algebraic independence for values of integral curves |
| work_keys_str_mv | AT fonsecat algebraicindependenceforvaluesofintegralcurves |