Chirskii, V. G. Arithmetic properties of Euler series. (English. Russian original) Zbl 1330.11047 Mosc. Univ. Math. Bull. 70, No. 1, 41-43 (2015); translation from Vestn. Mosk. Univ., Ser. I 70, No. 1, 59-61 (2015). Summary: A lower bound for the \(p\)-adic valuation of the number \(E_p= \Sigma_{n=1}^{\infty}n! \in \mathbb Q_p\) defined by an Euler-type series is proved in the paper for infinitely many prime numbers \(p\). Cited in 7 Documents MSC: 11J61 Approximation in non-Archimedean valuations 11J72 Irrationality; linear independence over a field 11J85 Algebraic independence; Gel’fond’s method 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain 34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms Keywords:Euler series; \(p\)-adic valuation PDFBibTeX XMLCite \textit{V. G. Chirskii}, Mosc. Univ. Math. Bull. 70, No. 1, 41--43 (2015; Zbl 1330.11047); translation from Vestn. Mosk. Univ., Ser. I 70, No. 1, 59--61 (2015) Full Text: DOI References: [1] V. G. Chirskii, “On Global Relations,” Matem. Zametki 48(2), 123 (1990). · Zbl 0764.11031 [2] D. Bertrand, V. Chirskii, and J. Yebbon, “Effective Estimates for Global Relations on Euler-Type Series,” Ann. Fac. Sci. Toulouse XIII(2), 241 (2004). · Zbl 1176.11036 · doi:10.5802/afst.1069 [3] Yu. V. Nesterenko, “Hermite-Pade Approximations of Generalized Hypergeometric Functions,” Matem. Sborn, 185(10), 39 (1994). · Zbl 0849.11052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.