# Journal of the Ramanujan Mathematical Society

Volume 31, Issue 2, June 2016 pp. 125–135.

Generalization of an identity of Ramanujan

**Authors**:
Sanoli Gun and M. Ram Murty

**Author institution:**Institute for Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600 113, India

**Summary: **
In this article, we extend two identities proved by Ramanujan
involving the Riemann zeta function and the Dirichlet L-function
associated to the non-trivial Dirichlet character modulo 4. More
precisely, given two power series
∑ n=0 ∞ an Tn and ∑ n = 0 ∞
bn Tn
which are both rational functions with certain property,
we then explicitly show that
∑ n=0 ∞ an bn Tn
is again a rational function with the same property. We use this
to explain Ramanujan's identities and also analyse Rankin-Selberg
convolutions of automorphic L-functions.

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