论文标题
艾森斯坦系列和史塔克·赫纳点的限制
Restriction of Eisenstein series and Stark-Heegner points
论文作者
论文摘要
在达尔蒙（Darmon），波兹（Pozzi）和冯克（Vonk）的最新作品中，作者考虑了希尔伯特·艾森斯坦（Hilbert Eisenstein）系列的特定$ p $ - 阿迪克家族$ e_k（1，\ brch）$与奇数角色$ \ brch $相关的狭窄理想级别$ \ brch $相关的理想小组组的真实Quadratic field $ f $，并计算了某个$ p $ $ $ $ $ $ $ - $ e_k（1，\ brch）$和椭圆形的新形式$ f $ of $γ_0（p）$ $ 2 $。在本文中，我们将其构造概括为包括环体变量，从而获得两种可变的三重产品$ p $ -Adic $ l $ - 系列。此外，当$ f $与$ \ q $上的椭圆曲线$ e $相关时，我们证明，沿重量方向，这款$ p $ -Adic $ l $ -series的第一个衍生物是$ p $ a的$ e $ $ e $ $ f $ $ $ $ $ $ $ $ p $ p $ p $ $ p $ - $ p $ -
In a recent work of Darmon, Pozzi and Vonk, the authors consider a particular $p$-adic family of Hilbert Eisenstein series $E_k(1,\brch)$ associated with an odd character $\brch$ 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 $E_k(1,\brch)$ 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 $E$.
