Mean values of multiplicative functions on shifted numbers
type: Item
instance of: scholarly article
title: Mean values of multiplicative functions on shifted numbers
zbMATH Open document ID: 0932.11059
DOI: 10.1007/BF02465584
published in: Lithuanian Mathematical Journal
publication date: 1999-06-14T00:00:00Z
review text: 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 \(x\rightarrow \infty \).
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 1296190
zbMATH Keywords: sums of multiplicative functions
zbMATH Keywords: mean values
zbMATH Keywords: multiplicative functions on shifted numbers
zbMATH Keywords: asymptotic formula
author: Gediminas Stepanauskas
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1296190