- Title
- On the transcendence degree of the differential field generated by Siegel modular forms
- Creator
- Bertrand, D.; Zudilin, W.
- Relation
- Journal fuer die Reine und Angewandte Mathematik: Crelle's journal Vol. 554, p. 47-68
- Publisher Link
- http://dx.doi.org/10.1515/crll.2003.008
- Publisher
- De Gruyter
- Resource Type
- journal article
- Date
- 2003
- Description
- It is a classical fact that the elliptic modular function λ=(ϑ₁₀/ϑ₀₀)⁴ satisfies an algebraic differential equation of order 3 (this goes back to Jacobi’s Fundamenta nova), and none of lower order (cf. [Ra], [M]). In this paper, we show how these properties generalize to Siegel modular functions of arbitrary degree.
- Subject
- transcendence degree; algebraic differential equation; Siegel modular functions
- Identifier
- http://hdl.handle.net/1959.13/803687
- Identifier
- uon:6477
- Identifier
- ISSN:0075-4102
- Rights
- The final publication is available at www.degruyter.com
- Language
- eng
- Full Text
- Reviewed
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|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Publisher version (open access) | 189 KB | Adobe Acrobat PDF | View Details Download |