Hall 123

Partial sums of arithmetical functions in the context of the theory of Ramanujan expansions.

Biswajyoti Saha

IMSc

For an arithmetical function f,we study its growth in terms of its partial sums $F(x):= \sum_{n \le x} f(n)$.In this lecture,we will discuss some classical methods of estimating such partial sums and then will see how the theory of Ramanujan expansions can be used to give estimates on the partial sums of arithmetical functions with absolutely convergent Ramanujan expansion.