English

On approximation measures of $q$-exponential function

Number Theory 2015-08-18 v1

Abstract

We shall present effective approximations measures for certain infinite products related to qq-exponential function. There are two main targets. First we shall prove an explicit irrationality measure result for the values of qq-exponential function at rational points. Then, if we restrict the approximations to rational numbers of the shape ds/Nd^s/N, we may replace Bundschuh's irrationality exponent 7/37/3 by 2+13+23=2.1547...2+\frac{1}{3+2\sqrt 3}=2.1547....

Keywords

Cite

@article{arxiv.1412.4115,
  title  = {On approximation measures of $q$-exponential function},
  author = {Leena Leinonen and Marko Leinonen and Tapani Matala-aho},
  journal= {arXiv preprint arXiv:1412.4115},
  year   = {2015}
}
R2 v1 2026-06-22T07:29:40.135Z