Choose logarithms of nonzero algebraic numbers $\alpha_1,\ldots,\alpha_n$ and algebraic numbers $\beta_0,\ldots,\beta_n$, and put
$$
\Lambda=\beta_0+\sum_{j=1}^n\beta_j\log\alpha_j.
$$
Let $A_j$ bound $10$, the <naive polynomial height> of the minimal polynomial of $\alpha_j$, and $\exp(|\log\alpha_j|)$. Let $B$ bound all the corresponding heights of the $\beta_j$ and all $\log A_j$. There is an effective constant $C$, depending only on $n$ and the degree of the number field generated by the data, such that
$$
\Lambda\ne0
\quad\Longrightarrow\quad
|\Lambda|>\exp\!\left(-C\prod_{j=1}^n\log A_j\,\log B\right).
$$


 General lower bound for a linear form in logarithms

ID: general-lower-bound-for-a-linear-form-in-logarithms