8 papers
Two identities involving Cohen-Ramanujan expansions
Arya Chandran, K Vishnu Namboothiri
An arithmetical function is said to admit a \emph{Cohen-Ramanujan expansion} , if the series on the right hand side converges for…
Some asymptotic formulae involving Cohen-Ramanujan expansions
Arya Chandran, Vishnu Namboothiri K
Cohen-Ramanujan sum, denoted by , is an exponential sum similar to the Ramanujan sum . An arithm…
A Menon-type Identity derived using Cohen-Ramanujan sum
Arya Chandran, K Vishnu Namboothiri
Menon's identity is a classical identity involving gcd sums and the Euler totient function . We derived the Menon-type identity $\sum\limits_{\substack{m=1\\(m.n^s)_s=1}}^{n^s}…
Some asymptotic formulae involving Cohen-Ramanujan expansions
Arya Chandran, K Vishnu Namboothiri
Some necessary and sufficient conditions for the existence of Cohen-Ramanujan expansions for arithmetical functions were provided by these authors in [\textit{arXive preprint arXiv…
On a Ramanujan type expansion of arithmetical functions
Arya Chandran, K Vishnu Namboothiri
Srinivasa Ramanujan provided series expansions of certain arithmetical functions in terms of the exponential sums defined by $c_r(n) = \sum\limits_{\substack{{m=1}\\ (m,r)=1}}^{r}…
On two mean square averages of Dirichlet -function
Neha Elizabeth Thomas, Arya Chandran, K Vishnu Namboothiri
Finding the mean square averages of the Dirichlet -functions over Dirichlet characters of same parity is an active problem in number theory. Here we explicitly evaluate such…