On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression (Q713176)

In the paper under review, using the Hardy-Littlewood circle method, the author proves a Bombieri-Vinogradov type theorem for the Waring-Goldbach problem with one prime variable restricted to a residue class. The major arc contribution is treated by a use of the Bombieri-Vinogradov theorem, and the author generalizes the treatment of the major arcs terms. In order to evaluate the minor arcs contribution, the author employs the strategy of \textit{K. Halupczok} [J. Number Theory 117, No. 2, 292--300 (2006; Zbl 1099.11058)]. Note that one can give a new improvement of the result in this paper by using \textit{T. D. Wooley}'s recent article on efficient congruencing [Ann. Math. (2) 175, No. 3, 1575--1627 (2012; Zbl 1267.11105)].