In this paper the author considers a particular type of polynomials with integer coefficients, consisting of a perfect power and two norm forms of abelian number fields with coprime discriminants. It is shown that such a polynomial represents every natural number with only finitely many exceptions. The circle method is used, and the local class field theory played a central role in estimating the singular series.
"Almost universality of a sum of norms." Hiroshima Math. J. 46 (1) 55 - 77, March 2016. https://doi.org/10.32917/hmj/1459525930