  A cubic (resp. biquadratic) theta series is a power series whose n-th
coefficient is equal to 1 if n is a perfect cube (resp. fourth power) and zero
otherwise. We improve on a result of Bradshaw by showing that such series is
not a cubic (resp. biquadratic) algebraic number when evaluated at reciprocals
of integers. The proof relies on a "nested gaps technique" for linear
independence and on recent results by the author on Waring's problem for cubes
and biquadrates.
