Mean values of multiplicative functions on shifted numbers
An asymptotic formula is given, with an estimate for the remainder term, for certain sums of type \( \sum _{p\leq x} g_1(p+2) g_2(p+1)\). Here \(g_j\) denote multiplicative functions satisfying \( |g_j(n) |\leq 1\). We get a nontrivial estimate if the sums \( \sum p^{-1} |g_j(p)-1 |^2 \) do not diverge ``too fast'', which means that the sums for \( \log x < p < x \) must tend to 0 as \(x\rightarrow \infty \).
multiplicative functions on shifted numbers
scientific article; zbMATH DE number 1296190
scientific article