@Article{Zaccagnini1992b,
  Author = "A. Zaccagnini",
  Title  = "On the exceptional set for the sum of a prime and a $k-$th power",
  Journal = "Mathematika",
  Volume = 39,
  Pages = "400--421",
  Year = 1992,
  Abstract = "Let $k\ge 2$ be an integer, and set 
    $E_k(X) := |\{ n \le X\colon$ $n\ne m^k$, 
    $n$ is not a sum of a prime and a $k$-th power$\}|$. 
    We prove that there exists $\delta = \delta(k)>0$ such that 
    $E_k(X) \ll_k X^{1-\delta}$, by means of a suitable application of the 
    circle method, essentially a variant of Montgomery \& Vaughan's method 
    (Acta Arithmetica 1975). 
    The proof is similar to the one given by Br{\"u}nner, Perelli \& Pintz 
    (Acta Math. Hungarica 1989) in the case $k=2$, the main new difficulty 
    being in the treatment of the singular series."
}