Some properties and applications of a new arithmetic function in analytic number theory

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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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

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

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Cite this paper

APA

Muthumalai, 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.

Chicago

Muthumalai, 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.

MLA

Muthumalai, 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.

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