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Cancellation of factorials. (English. Russian original) Zbl 1030.11032
Sb. Math. 192, No. 8, 1181-1207 (2001); translation from Mat. Sb. 192, No. 8, 95-122 (2001).
It is well-known that for any positive integer, the differential operator \((1/n!)(d/d z)^n\) maps the polynomial ring \({\mathbb Z}[z]\) to itself. This is the most basic example of the phenomenon of cancellation of factorials. This paper deals with explicit generalizations of this phenomenon to various operators defined over certain rings, such as the ring of integers \(\mathcal{O}_K\) of a number field \(K\), or the ring of matrices with entries in \(\mathcal{O}_K\). In particular, this enables the author to present a refined irrationality measure for values of certain \(G\)-functions.

MSC:
11J91 Transcendence theory of other special functions
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