Abstract
We study the lacunary Dirichlet series obtained from the reciprocals of s th powers of balancing numbers. This function admits an analytic continuation to the entire complex plane. The series converges to irrational numbers at odd negative integral arguments. Finally, we also study the analytic continuation of the balancing L-function.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. André-Jeannin, Irrationaliré de Ia somme des inverses de certaines suites recurrentes, C. R. Acad. Sci. Paris, Ser. I, 308 (1989), 539–541.
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag (1976).
A. Behera and G. K. Panda, On the square roots of triangular numbers, Fib. Quan., 37(2) (1999), 98–105.
K. Cbandrasekharan, Introduction to Analytic Number Theory, Springer-verlag, New York, (1968).
D. Duverney, Ke. Nishioka, Ku. Nishioka and I. Shiokawa, Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers, Proc. Japan Acad. Ser. A Math. Sci., 73 (1997), 140–142.
C. Elsner, S. Shimomura and I. Shiokawa, Algebraic relations for reciprocal sums of Fibonacci numbers, Acta Arith., 130 (2007), 37–60.
L. Navas, Analytic continutation of the Fibonacci Dirichlet series, Fib. Quan., 39 (2001), 409–418.
M. Ram Murty, Fibonacci zeta function, Automorphic Representations and L-Functions, TIFR Conference Proceedings, edited by D. Prasad, C.S. Rajan, A. Sankaranarayanan, J. Sengupta, Hindustan Book Agency, New Delhi, India (2013).
J. P. Serre, A course in arithmetic, Springer-Verlag, New York, Heidelberg (1973).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rout, S.S., Panda, G.K. Balancing Dirichlet series and related L-functions. Indian J Pure Appl Math 45, 943–952 (2014). https://doi.org/10.1007/s13226-014-0097-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-014-0097-0