Room 326

Correlation of multiplicative functions.

Pranendu Darbar

IMSc

In the first part of this talk, we will discuss about the
asymptotic behavior of the correlation of multiplicative functions
which is the mean of product of multiplicative functions on shifted
arguments over integers. We will give some of its consequences. In the
final part, we will discuss about the asymptotic formula of the
correlation functions over polynomial ring $\mathbb{F}_q[x]$. As a
consequences, we get that the correlation of truncated Liouville
function over shifted polynomials is small and also the distribution
of the sum of additive function over $\mathbb{F}_q[x]$.