• A Menon-type identity concerning Dirichlet characters and a generalization of the gcd function

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/131/0018

• # Keywords

Menon-type identity; Dirichlet character; generalized gcd; Klee’s function.

• # Abstract

Menon’s identity is a classical identity involving gcd sums and the Eulertotient function $\phi$. In a recent paper, Zhao and Cao (Int. J. Number Theory 13(9) (2017) 2373--2379) derived the Menon-type identity $\sum ^n_{k=1}(k −1, n)\chi(k) = \phi(n)\tau (\frac{n}{d})$, where $\chi$ is a Dirichlet character $\mod n$ with conductor $d$. We derive an identity similar to this replacing gcd with a generalization it. We also show that some of the arguments used in the derivation of Zhao--Cao identity can be improved if one uses the method we employ here.

• # Author Affiliations

1. Department of Mathematics, University College, Thiruvananthapuram 695 034, India
2. Department of Mathematics, Government College, Ambalapuzha 688 561, India
3. Department of Mathematics, SD College, Alappuzha 688 003, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019