论文标题
Eisenstein系列，P-Adic模块化功能和过度融合
Eisenstein series, p-adic modular functions, and overconvergence
论文作者
论文摘要
令$ p $为Prime $ \ ge 5 $。我们为“ Eisenstein家族”成员建立了明确的过度转换率，特别是对于$ p $ -Adic模块化函数$ v（e _ {（1,0,0）}^{\ ast}）/e _ {（1,0）科尔曼的模块化形式的$ p $ addic家族的理论。证明是通过深入分析$ v（e_k）/e_k $的$ p $ addic模块化函数的过度授权速率进行的，其中$ e_k $是经典的Eisenstein系列级别$ 1 $ $ 1 $和$ k $ $ k $ averisible $ p-1 $。在某些条件下，我们将后者的结果扩展到Coleman定理的广泛概括 - 关于$ v（e_ {p-1}）/e_ {p-1} $的过度授权率。我们还评论文献中先前的结果。其中包括我们的结果的应用程序$ 5 $和$ 7 $。
Let $p$ be a prime $\ge 5$. We establish explicit rates of overconvergence for members of the "Eisenstein family", notably for the $p$-adic modular function $V(E_{(1,0)}^{\ast})/E_{(1,0)}^{\ast}$ ($V$ the $p$-adic Frobenius operator) that plays a pi\-votal role in Coleman's theory of $p$-adic families of modular forms. The proof goes via an in-depth analysis of rates of overconvergence of $p$-adic modular functions of form $V(E_k)/E_k$ where $E_k$ is the classical Eisenstein series of level $1$ and weight $k$ divisible by $p-1$. Under certain conditions, we extend the latter result to a vast generalization of a theorem of Coleman--Wan regarding the rate of overconvergence of $V(E_{p-1})/E_{p-1}$. We also comment on previous results in the literature. These include applications of our results for the primes $5$ and $7$.
