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Izvestiya: Mathematics, 2001, Volume 65, Issue 4, Pages 659–672
DOI: https://doi.org/10.1070/IM2001v065n04ABEH000345 (Mi im345) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Derivatives of Siegel modular forms and exponential functions

D. Bertranda, W. V. Zudilinb

a Université Pierre & Marie Curie, Paris VI
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (217 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM2001v065n04ABEH000345
Abstract: We show that the differential field generated by Siegel modular forms and the differential field generated by exponentials of polynomials are linearly disjoint over $\mathbb C$. Combined with our previous work [3], this provides a complete multidimensional extension of Mahler's theorem on the transcendence degree of the field generated by the exponential function and the derivatives of a modular function. We give two proofs of our result, one purely algebraic, the other analytic, but both based on arguments from differential algebra and on the stability under the action of the symplectic group of the differential field generated by rational and modular functions.
Received: 26.12.2000
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2001, Volume 65, Issue 4, Pages 21–34
DOI: https://doi.org/10.4213/im345
Bibliographic databases:
Document Type: Article
MSC: Primary 11F46, 11J81; Secondary 12H05, 14K25, 42A16
Language: English
Original paper language: Russian
Citation: D. Bertrand, W. V. Zudilin, “Derivatives of Siegel modular forms and exponential functions”, Izv. RAN. Ser. Mat., 65:4 (2001), 21–34; Izv. Math., 65:4 (2001), 659–672
Citation in format AMSBIB
\Bibitem{BerZud01}
\by D.~Bertrand, W.~V.~Zudilin
\paper Derivatives of Siegel modular forms and exponential functions
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 21--34
\mathnet{http://mi.mathnet.ru/im345}
\crossref{https://doi.org/10.4213/im345}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1857708}
\zmath{https://zbmath.org/?q=an:1021.11013}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 659--672
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000345}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746781039}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:357
    Russian version PDF:184
    English version PDF:6
    References:43
    First page:1
     
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