In this article, we study the Beilinson–Bloch–Kato conjecture for motives associated to Rankin–Selberg products of conjugate self-dual automorphic representations, within framework Gan–Gross–Prasad conjecture. We show that if central critical value L-function does not vanish, then Bloch–Kato Selmer group with coefficients in a favorable field corresponding motive vanishes. also class constructe...

Abstract We prove an asymptotic expansion of the second moment central values $\mathrm {GL}(n)\times \mathrm {GL}(n)$ Rankin–Selberg L -functions $L(1/2,\pi \otimes \pi _0)$ for a fixed cuspidal automorphic representation $\pi _0$ over family $ with analytic conductors bounded by quantity that is tending to infinity. Our proof uses integral representations -functions, period regularised Eisenst...

Let π be a simple supercuspidal representation of the split even special orthogonal group. We compute Rankin-Selberg γ-factors for rank 1-twists by quadratic tamely ramified characters F*. Our results determine certain 1-dimensional summands Langlands parameter. Assuming an expected analogue work Blondel, Henniart, and Stevens, these completely parameter π.

In this paper we construct a Rankin-Selberg integral which represents the Spin10× St L-function attached to the groupGSO10×PGL2. We use this integral representation to give some equivalent conditions for a generic cuspidal representation on GSO10 to be a functorial lift from the group G2 × PGL2.