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We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G 0 = G 1 · ··· · G r , where each G i is a simple group of type A?, C?, D?, E6, or E7, we construct a differential equation over C(x) having Galois group G. 相似文献
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V. Kh. Salikhov 《Mathematical Notes》1998,64(2):230-239
For the hypergeometric function
satisfying a linear differential equation of ordert, for the case of an event prime to 3, a criterion is obtained for the algebraic independence over 2e of the numbers(k)/(),k=0, 1,..., t–1, where A {0}. The case of oddt was fully investigated in the author's previous papers.Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 273–284, August, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01854 and by the joint project of the INTAS foundation and the Russian Foundation for Basic Research. 相似文献
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Teresa Crespo 《代数通讯》2013,41(5):2089-2093
We characterize linear differential equations defined over a real differential field with a real closed field of constants C, which are solvable by real Liouville functions, as those having a differential Galois group whose identity component is solvable and C-split. 相似文献
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