Informatics Publishing Limited

Sanoli Gun ¹, M. Ram Murty ²

Affiliations
1 Institute for Mathematical Sciences, C.I.T Campus, Taramani, Chennai-600113, IN
2 Department of Mathematics, Queen’s University, Kingston, Ontario-K7L3N6, CA

Abstract

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

∑a_nTⁿ and ∑b_nTⁿ

which are both rational functions with certain property, we then explicitly show that

∑a_nb_nTⁿ

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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