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On Diophantine approximations of mock theta functions of third order. (English) Zbl 1001.11030
Summary: The paper gives bounds for the approximation of the values of Ramanujan’s mock theta functions of third order and more generally of some \(q\)-hypergeometric functions by the elements of an algebraic number field. Simultaneous approximations for the values of the \(q\)-exponential function are also obtained. All the results are given both in the Archimedean and \(p\)-adic case.

MSC:
11J82 Measures of irrationality and of transcendence
11J61 Approximation in non-Archimedean valuations
11J72 Irrationality; linear independence over a field
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