‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

Inspired by Sun’s breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups GLn(R)×GLn−1(R) and GLn(C)×GLn−1(C), we confirm it for GLn(C)×GLn(C) at the central critical point.

(Under the Riemann Hypothesis the stronger bound |ζ(1 + it)| ≥ c log log t holds.) From a modern point of view, the method of de la Vallée Poussin is based on Rankin-Selberg convolutions and a positivity argument (an effective version of Landau’s Lemma – see [HL94, Appendix]). It can be applied to any Rankin-Selberg L-function L(s, π1 ⊗ π2), provided that one of the πi’s is self-dual (cf. [Sar0...

The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this ...