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Some application of a new mean value theorem on Riemann’s \(\zeta\)- function. (Chinese. English summary) Zbl 0702.11055

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

Citations:

Zbl 0506.10032
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