Rankin-Selberg L-functions and "beyond Endoscopy" II

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Research Article

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Journal of the Ramanujan Mathematical Society


Suppose f and g are Hecke cusp forms on SL2(Z), where f is holomorphic and g is either a holomorphic form or a Maaß form. We assume both f and g are eigenfunctions of all the Hecke operators. Using Langlands' "Beyond Endoscopy" approach, we prove that the Rankin-Selberg convolution L(s, f × g) admits holomorphic extension to the region Rs > 1/2 unless g = f, in which case the L-function has a pole at s = 1 with residue {equation presented}, where || f || is the Petersson norm of f and k is the weight of f.

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