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Transcendental values of the \(p\)-adic digamma function. (English) Zbl 1253.11077
Summary: We study the \(p\)-adic analogue of the digamma function, which is the logarithmic derivative of the classical \({\Gamma}\)-function. We apply the \(p\)-adic theory of linear forms in logarithms to establish transcendence of \(p\)-adic analogues of the classical Euler and Euler–Lehmer constants.

MSC:
11J86 Linear forms in logarithms; Baker’s method
11J91 Transcendence theory of other special functions
11S40 Zeta functions and \(L\)-functions
33B15 Gamma, beta and polygamma functions
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