Ramesh Kumar Muthumalai

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

Volume 17, 2011, Number 3, Pages 38—48

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## Details

### Authors and affiliations

Ramesh Kumar Muthumalai

*Department of Mathematics, D.G. Vaishnav College
Chennai-600 106, Tamil Nadu, India
*

### Abstract

We introduce an arithmetic function and study some of its properties analogous to Möbius function in analytic number theory. In addition, we derive some simple expressions to connect infinite series and infinite products through this new arithmetic function. Moreover, we study applications of this new function to derive simple identities on partition of an integer and some special infinite products in terms of multiplicative functions.

### Keywords

- Möbius function
- Infinite product
- Lambert series
- Arithmetic function
- Partition
- Divisor function

### AMS Classification

- 11A25
- 11K65
- 05A17
- 11P82
- 40A20

### References

- Andrews, G. E. Number Theory , W. B. Saunders Co., Philadelphia, 1971.
- Andrews, G. E, The Theory Partitions, Cambridge University Press, UK, 1998.
- Andrews, G. E, Eriksson K, Integer Partitions, Cambridge University Press, UK, 2004.
- Apostal, T. M. Introduction to Analytic Number Theory, Springer International Student Edition, New York (1989).
- Bateman, P. T, H. G. Diamond. Analytic Number Theory, World Scientific Publishing Co Ltd, USA, 2004.
- Gradshteyn, I. S, I. M. Ryzhik. Tables of Integrals, Series and Products, 6 Ed , Academic Press (2000), USA
- Sándor, J., B. Crstici. Handbook of Number Theory II, Springer, Kluwer Acedemic Publishers, Netherland, 2004.

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## Cite this paper

APAMuthumalai, R. K. (2011). Some properties and applications of a new arithmetic function in analytic number theory. Notes on Number Theory and Discrete Mathematics, 17(3), 38-48.

ChicagoMuthumalai, Ramesh Kumar. “Some Properties and Applications of a New Arithmetic Function in Analytic Number Theory.” Notes on Number Theory and Discrete Mathematics 17, no. 3 (2011): 38-48.

MLAMuthumalai, Ramesh Kumar. “Some Properties and Applications of a New Arithmetic Function in Analytic Number Theory.” Notes on Number Theory and Discrete Mathematics 17.3 (2011): 38-48. Print.