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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
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
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
Linking options:
https://www.mathnet.ru/eng/im345https://doi.org/10.1070/IM2001v065n04ABEH000345 https://www.mathnet.ru/eng/im/v65/i4/p21
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Abstract page: | 357 | Russian version PDF: | 184 | English version PDF: | 6 | References: | 43 | First page: | 1 |
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