6 papers
On near orthogonality of certain -vectors involving generalized Ramanujan sums
Neha Elizabeth Thomas, K Vishnu Namboothiri
The near orthgonality of certain -vectors involving the Ramanujan sums were studied by E. Alkan in [J. Number Theory, 140:147--168 (2014)]. Here we undertake the study of simila…
A computable formula for evaluating the mean square sum of -functions
Neha Elizabeth Thomas, K Vishnu Namboothiri
For Dirichlet characters mod where , we here give a computable formula for evaluating the mean square sums $\sum\limits_{\substack{χ\text{ mod }k\\χ(-1)=(-1)^r}}|L…
On an exponential power sum
Neha Elizabeth Thomas, K Vishnu Namboothiri
Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power sum with negative powers in terms of another exponential power sum with positive…
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…
A Menon-type Identity concerning Dirichlet characters and a generalization of the gcd function
Arya Chandran, Neha Elizabeth Thomas, K Vishnu Namboothiri
Menon's identity is a classical identity involving gcd sums and the Euler totient function . In a recent paper, Zhao and Cao derived the Menon-type identity $\sum\limits_{\subst…
A Menon-type identity using Klee's function
Arya Chandran, Neha Elizabeth Thomas, K Vishnu Namboothiri
Menon's identity is a classical identity involving gcd sums and the Euler totient function . A natural generalization of is the Klee's function . In this paper we deriv…