| Summary: | In the early 90’s, Perrin-Riou [PR] introduced an important refinement of the Mazur-Swinnerton-Dyer p-adic L-function of an elliptic curve E over Q, taking values in its p-adic de Rham cohomology. She then formulated a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for this p-adic L-function, in which the formal group logarithms of global points on E make an intriguing appearance. The present work extends Perrin-Riou’s construction to the setting of a Garret-Rankin triple product (f, g, h), where f is a cusp form of weight two attached to E and g and h are classical weight one cusp forms with inverse nebentype characters, corresponding to odd two-dimensional Artin representations %g and %h respectively. The resulting p-adic Birch and Swinnerton-Dyer conjecture involves the p-adic logarithms of global points on E defined over the field cut out by %g ⊗ %h, in the style of the regulators that arise in [DLR1], and recovers Perrin-Riou’s original conjecture when g and h are Eisenstein series.
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