Ramesh Kumar Muthumalai

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 2, Pages 8—14

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## Details

### Authors and affiliations

Ramesh Kumar Muthumalai

*Department of Mathematics, Saveetha Engineering College
Saveetha Nagar, Thandalam, Chennai–602 105, Tamil Nadu, India *

### Abstract

Some identities for infinite series involving arithmetic functions are derived through Jacobi symbols (−1|*k*) and (2|*k*). Using these identities, some Dirichlet series are expressed in terms of Hurwitz zeta function.

### Keywords

- Möbius function
- Arithmetic function
- Jacobi symbol
- Dirichlet series

### AMS Classification

- 11A25

### References

- Apostal, T. M. (1989) Introduction to Analytic Number Theory, Springer International StudentEdition, New York.
- Gradshteyn, I. S. & Ryzhik, I. M. (2000) Tables of Integrals, Series and Products, 6 Ed,Academic Press, USA.
- Ireland, K. & Rosen, M. (1990) A Classical Introduction to Modern Number Theory, 2Ed,Springer-Verlag, New York.
- Sandor, J. & Crstici, B. (2004) Handbook of Number Theory II, Springer, Kluwer AcedemicPublishers, Netherland.

## Related papers

## Cite this paper

APAMuthumalai, R. K. (2015). Some infinite series involving arithmetic functions. Notes on Number Theory and Discrete Mathematics, 21(2), 8-14.

ChicagoMuthumalai, Ramesh Kumar. “Some Infinite Series Involving Arithmetic Functions.” Notes on Number Theory and Discrete Mathematics 21, no. 2 (2015): 8-14.

MLAMuthumalai, Ramesh Kumar. “Some Infinite Series Involving Arithmetic Functions.” Notes on Number Theory and Discrete Mathematics 21.2 (2015): 8-14. Print.