Yao, Qi; He, Jiyu Some application of a new mean value theorem on Riemann’s \(\zeta\)- function. (Chinese. English summary) Zbl 0702.11055 J. Math., Wuhan Univ. 9, No. 2, 187-192 (1989). The authors apply the estimate of the power mean-values for the Riemann zeta-function due to J.-M. Deshouillers and H. Iwaniec [Mathematika 29, 202-212 (1982; Zbl 0506.10032)] to estimate the sum \(\sum_{1\leq r\leq k}| g(c+it_ r)|,\) where g(s) is a product of sums of the form \(\sum_{N<n\leq 2N}a_ n/n^ s\). It is claimed that the estimate gives better results concerning the difference between consecutive primes, but the reviewer cannot follow the condensed and poorly presented argument. Reviewer: P.Shiu MSC: 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 11N05 Distribution of primes 11M41 Other Dirichlet series and zeta functions Keywords:power mean-values; Riemann zeta-function; difference between consecutive primes Citations:Zbl 0506.10032 PDFBibTeX XMLCite \textit{Q. Yao} and \textit{J. He}, J. Math., Wuhan Univ. 9, No. 2, 187--192 (1989; Zbl 0702.11055)