On Baker type lower bounds for linear forms

A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers $1,\Theta_1,...,\Theta_m\in\mathbb{C}^*$ over the ring $\mathbb{Z}_{\mathbb{I}}$ of an imaginary quadratic field $\mathbb{I}$. This work deals with the simultaneous auxiliary functions case

Explicit irrationality measures for continued fractions

AbstractLet τ=[a0;a1,a2,…], a0∈N, an∈Z+, n∈Z+, be a simple continued fraction determined by an infinite integer sequence (an). We are interested in finding an effective irrationality measure as explicit as possible for the irrational number τ. In particular, our interest is focused on sequences (an) with an upper bound at most (ank), where a>1 and k>0. In addition to our main target, arithmetic of continued fractions, we shall pay special attention to studying the nature of the inverse function z(y) of y(z)=zlogz