#### 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 $\mathbb{F}_q[x]$.

Done