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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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