PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Triple correlations of multiplicative functions

Volume 180 / 2017

Pranendu Darbar Acta Arithmetica 180 (2017), 63-88 MSC: Primary 11N37; Secondary 11N60. DOI: 10.4064/aa8605-4-2017 Published online: 1 August 2017


We find an asymptotic formula for the following sum with explicit error term: \[M_{x}(g_{1}, g_{2}, g_3)=\frac{1}{x}\sum_{n\le x}g_{1}(F_1(n))g_{2}(F_2(n))g_{3} (F_3(n)),\] where $F_1(x), F_2(x)$ and $F_3(x)$ are polynomials with integer coefficients and $g_1,g_2,g_3$ are multiplicative functions with modulus less than or equal to $1.$

Moreover, under some assumption on $g_1,g_2,$ we prove that as $x\rightarrow \infty,$ \[\frac{1}{x}\sum_{n\le x}g_1(n+3)g_2(n+2)\mu(n+1)=o(1),\] and assuming the $2$-point Chowla type conjecture we show that as $x\rightarrow \infty,$ \[\frac{1}{x}\sum_{n\le x}g_1(n+3)\mu(n+2)\mu(n+1)=o(1).\]


  • Pranendu DarbarInstitute of Mathematical Sciences
    CIT Campus, Taramani
    Chennai 600113, India
    Homi Bhabha National Institute
    Training School Complex
    Anushakti Nagar
    Mumbai 400094, India

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image