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Generalization of an Identity of Ramanujan
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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
∑anTn and ∑bnTn
which are both rational functions with certain property, we then explicitly show that
∑anbnTn
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.
∑anTn and ∑bnTn
which are both rational functions with certain property, we then explicitly show that
∑anbnTn
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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