Restriction of Eisenstein series and Stark–Heegner points

Abstract

In a recent work of Darmon, Pozzi and Vonk, the authors consider a particular p-adic family of Hilbert–Eisenstein series E k (1,ϕ) associated with an odd character ϕ of the narrow ideal class group of a real quadratic field F and compute the first derivative of a certain one-variable twisted triple product p-adic L-series attached to E k (1,ϕ) and an elliptic newform f of weight 2 on Γ 0 (p). In this paper, we generalize their construction to include the cyclotomic variable and thus obtain a two-variable twisted triple product p-adic L-series. Moreover, when f is associated with an elliptic curve E over ℚ, we prove that the first derivative of this p-adic L-series along the weight direction is a product of the p-adic logarithm of a Stark–Heegner point of E over F introduced by Darmon and the cyclotomic p-adic L-function for E.