Let 0 lambda x + delta mod 1, where 0 <= delta < 1. Let rho be the rotation number of the map f(delta). We will give some numerical relations between the values of lambda,delta and rho, essentially using Hecke-Mahler series and a tree structure. When both parameters lambda and delta are algebraic numbers, we show that rho is a rational number. Moreover, in the case lambda and delta are rational, we give an explicit upper bound for the height of rho under some assumptions on lambda.