Triple correlations of multiplicative functions
Tom 180 / 2017
Acta Arithmetica 180 (2017), 63-88
MSC: Primary 11N37; Secondary 11N60.
DOI: 10.4064/aa8605-4-2017
Opublikowany online: 1 August 2017
Streszczenie
We find an asymptotic formula for the following sum with explicit error term: 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).