A note on sums of five almost equal prime squares
\textit{L. K. Hua} proved in [Q. J. Math., Oxf. Ser. 9, 68-80 (1938; Zbl 0018.29404)] that every sufficiently large integer \(N\equiv 5\pmod{24}\) is the sum of five prime squares. In this paper, the author shows that these primes can be restricted to short intervals of the form \([\sqrt{N/5}- U,\sqrt{N/5}+ U]\), where \(U= N^{9/20+\varepsilon}\) under the GRH and \(U= N^{1/2-\delta}\) unconditionally. The proof of this result uses the circle method and follows the techniques developed in two previous papers by \textit{M. C. Liu} and \textit{K. M. Tsang} [Monatsh. Math. 111, 147-169 (1991; Zbl 0719.11064) and in Théorie des nombres, C. R. Conf. Int., Quebec/Can. 1987, 595-624 (1989; Zbl 0682.10043)]. On the minor arcs, the contribution is bounded by an estimation for the exponential sum \(\sum_{x<n\leq x+y}\Lambda(n)e(n^2\alpha)\) given by \textit{J. Y. Liu} and \textit{T. Zhan} [Acta Arith. 77, 369-383 (1996; Zbl 0863.11067)].
scientific article; zbMATH DE number 1052892