Some infinite series involving arithmetic functions

Ramesh Kumar Muthumalai
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 2, Pages 8–14
Full paper (PDF, 172 Kb)

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

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