Simultaneous rational approximation via Rickert's integrals

Using Rickert's contour integrals, we give effective lower bounds for simultaneous rational approximations to numbers in the sets{(1−aN)ν,(1+aN)ν}and{(1+aN)ν,(1+2aN)ν}. Here N>a≥1 are integers, 0<ν<1 is a rational number and at least one of the radicals is irrational in each set. The result is valid for all q≥1 where q denotes the denominator of the approximating rational number.