Matches in SemOpenAlex for { <https://semopenalex.org/work/W1990804711> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W1990804711 endingPage "6279" @default.
- W1990804711 startingPage "6279" @default.
- W1990804711 abstract "Define the Liouville function for $A$, a subset of the primes $P$, by $lambda _{A}(n) =(-1)^{Omega _A(n)}$, where $Omega _A(n)$ is the number of prime factors of $n$ coming from $A$ counting multiplicity. For the traditional Liouville function, $A$ is the set of all primes. Denote [ L_A(x):=sum _{nleq x}lambda _A(n)quad mbox {and}quad R_A:=lim _{nto infty }frac {L_A(n)}{n}.] It is known that for each $alpha in [0,1]$ there is an $Asubset P$ such that $R_A=alpha$. Given certain restrictions on the sifting density of $A$, asymptotic estimates for $sum _{nleq x}lambda _A(n)$ can be given. With further restrictions, more can be said. For an odd prime $p$, define the characterâlike function $lambda _p$ as $lambda _p(pk+i)=(i/p)$ for $i=1,ldots ,p-1$ and $kgeq 0$, and $lambda _p(p)=1$, where $(i/p)$ is the Legendre symbol (for example, $lambda _3$ is defined by $lambda _3(3k+1)=1$, $lambda _3(3k+2)=-1$ ($kgeq 0$) and $lambda _3(3)=1$). For the partial sums of characterâlike functions we give exact values and asymptotics; in particular, we prove the following theorem. Theorem. If $p$ is an odd prime, then [ max _{nleq x} left |sum _{kleq n}lambda _p(k)right | asymp log x.] This result is related to a question of ErdÅs concerning the existence of bounds for numberâtheoretic functions. Within the course of discussion, the ratio $phi (n)/sigma (n)$ is considered." @default.
- W1990804711 created "2016-06-24" @default.
- W1990804711 creator A5029261392 @default.
- W1990804711 creator A5029379712 @default.
- W1990804711 creator A5046677225 @default.
- W1990804711 date "2010-12-01" @default.
- W1990804711 modified "2023-10-18" @default.
- W1990804711 title "Completely multiplicative functions taking values in ${-1,1}$" @default.
- W1990804711 cites W1489006728 @default.
- W1990804711 cites W1489746200 @default.
- W1990804711 cites W187679133 @default.
- W1990804711 cites W1985549462 @default.
- W1990804711 cites W2010630473 @default.
- W1990804711 cites W2023411861 @default.
- W1990804711 cites W2039862726 @default.
- W1990804711 cites W2056806689 @default.
- W1990804711 cites W2077216373 @default.
- W1990804711 cites W2113268225 @default.
- W1990804711 cites W2146844680 @default.
- W1990804711 cites W2477451100 @default.
- W1990804711 cites W2479782962 @default.
- W1990804711 cites W3175367423 @default.
- W1990804711 cites W586135738 @default.
- W1990804711 cites W637040980 @default.
- W1990804711 cites W854030682 @default.
- W1990804711 doi "https://doi.org/10.1090/s0002-9947-2010-05235-3" @default.
- W1990804711 hasPublicationYear "2010" @default.
- W1990804711 type Work @default.
- W1990804711 sameAs 1990804711 @default.
- W1990804711 citedByCount "30" @default.
- W1990804711 countsByYear W19908047112012 @default.
- W1990804711 countsByYear W19908047112013 @default.
- W1990804711 countsByYear W19908047112014 @default.
- W1990804711 countsByYear W19908047112015 @default.
- W1990804711 countsByYear W19908047112016 @default.
- W1990804711 countsByYear W19908047112017 @default.
- W1990804711 countsByYear W19908047112018 @default.
- W1990804711 countsByYear W19908047112019 @default.
- W1990804711 countsByYear W19908047112020 @default.
- W1990804711 countsByYear W19908047112021 @default.
- W1990804711 countsByYear W19908047112022 @default.
- W1990804711 countsByYear W19908047112023 @default.
- W1990804711 crossrefType "journal-article" @default.
- W1990804711 hasAuthorship W1990804711A5029261392 @default.
- W1990804711 hasAuthorship W1990804711A5029379712 @default.
- W1990804711 hasAuthorship W1990804711A5046677225 @default.
- W1990804711 hasBestOaLocation W19908047111 @default.
- W1990804711 hasConcept C114614502 @default.
- W1990804711 hasConcept C121332964 @default.
- W1990804711 hasConcept C134306372 @default.
- W1990804711 hasConcept C156004811 @default.
- W1990804711 hasConcept C184992742 @default.
- W1990804711 hasConcept C2778113609 @default.
- W1990804711 hasConcept C2779557605 @default.
- W1990804711 hasConcept C30860621 @default.
- W1990804711 hasConcept C33923547 @default.
- W1990804711 hasConcept C42747912 @default.
- W1990804711 hasConcept C62520636 @default.
- W1990804711 hasConceptScore W1990804711C114614502 @default.
- W1990804711 hasConceptScore W1990804711C121332964 @default.
- W1990804711 hasConceptScore W1990804711C134306372 @default.
- W1990804711 hasConceptScore W1990804711C156004811 @default.
- W1990804711 hasConceptScore W1990804711C184992742 @default.
- W1990804711 hasConceptScore W1990804711C2778113609 @default.
- W1990804711 hasConceptScore W1990804711C2779557605 @default.
- W1990804711 hasConceptScore W1990804711C30860621 @default.
- W1990804711 hasConceptScore W1990804711C33923547 @default.
- W1990804711 hasConceptScore W1990804711C42747912 @default.
- W1990804711 hasConceptScore W1990804711C62520636 @default.
- W1990804711 hasIssue "12" @default.
- W1990804711 hasLocation W19908047111 @default.
- W1990804711 hasLocation W19908047112 @default.
- W1990804711 hasOpenAccess W1990804711 @default.
- W1990804711 hasPrimaryLocation W19908047111 @default.
- W1990804711 hasRelatedWork W1496306145 @default.
- W1990804711 hasRelatedWork W2266078656 @default.
- W1990804711 hasRelatedWork W2724394369 @default.
- W1990804711 hasRelatedWork W2898734283 @default.
- W1990804711 hasRelatedWork W2946044024 @default.
- W1990804711 hasRelatedWork W3129621902 @default.
- W1990804711 hasRelatedWork W3161659993 @default.
- W1990804711 hasRelatedWork W4231210283 @default.
- W1990804711 hasRelatedWork W4320926309 @default.
- W1990804711 hasRelatedWork W2923241701 @default.
- W1990804711 hasVolume "362" @default.
- W1990804711 isParatext "false" @default.
- W1990804711 isRetracted "false" @default.
- W1990804711 magId "1990804711" @default.
- W1990804711 workType "article" @default.