Leena Leinonen, Marko Leinonen, Tapani Matala-aho
Published 2014-12-12Version 1
We shall present effective approximations measures for certain infinite products related to $q$-exponential function. There are two main targets. First we shall prove an explicit irrationality measure result for the values of $q$-exponential function at rational points. Then, if we restrict the approximations to rational numbers of the shape $d^s/N$, we may replace Bundschuh's irrationality exponent $7/3$ by $2+\frac{1}{3+2\sqrt 3}=2.1547...$.
On the approximation of the values of exponential function and logarithm by algebraic numbers
Simultaneous approximation to values of the exponential function over the adeles
Rational approximations of the exponential function at rational points
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