Stark points on elliptic curves via Perrin-Riou’s philosophy

In the early 90’s, Perrin-Riou (Ann Inst Fourier 43(4):945–995, 1993) introduced an important refinement of Mazur–Swinnerton-Dyer p-adic L-function elliptic curve E over $$\mathbb {Q}$$ , taking values in its de Rham cohomology. She then formulated a analogue Birch and Swinnerton-Dyer conjecture for this L-function, which formal group logarithms global points on make intriguing appearance. The present work extends Perrin-Riou’s construction to setting Garret–Rankin triple product (f, g, h), where f is cusp form weight two attached g h are classical one forms with inverse nebentype characters, corresponding odd two-dimensional Artin representations $$\varrho _g$$ _h$$ respectively. resulting involves defined field cut out by _g\otimes \varrho style regulators that arise Darmon et al. (Forum Math 3(e8):95, 2015), recovers original when Eisenstein series.