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
Full paper (PDF, 189 Kb)

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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

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