Note on Legendre symbols connecting with certain infinite series

Ramesh Kumar Muthumalai
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 19, 2013, Number 2, Pages 77–83
Full paper (PDF, 143 Kb)

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Authors and affiliations

Ramesh Kumar Muthumalai
Department of Mathematics, D. G. Vaishnav College
Chennai–600106, Tamil Nadu, India

Abstract

Some applications of Legendre symbols connecting with certain infinite series are studied. In addition, some identities for Dirichlet series through Legendre symbols and Hurwitz zeta function are given.

Keywords

• Legendre symbols
• Infinite series
• Dirichlet series

AMS Classification

• 11A25
• 40A05

References

1. Apostal, T. M. Introduction to Analytic Number Theory, Springer International Student Edition, New York, 1989.
2. Gradshteyn, I. S., I. M. Ryzhik, Tables of Integrals, Series and Products (6th ed.), Academic Press, USA, 2000.
3. Muthumalai, R. K. Some properties of new arithmetic function and its applications to analytic number theory. Notes on Number Theory and Discrete Mathematics, Vol. 17, 2011, No. 3, 38–48.