Analytic continuation of overconvergent Hilbert eigenforms in the totally split case
Analytic continuation of overconvergent Hilbert eigenforms in the totally split case
复制标题
完全分裂情况下过收敛希尔伯特本征型的解析延拓
作者：
Shu Sasaki
本文将Buzzard，Taylor和Kassaei关于全实域F上p-adic过收敛Hilbert本征形的解析延拓的结果推广到全实域F上p-adic过收敛Hilbert本征形的情形，假设p在F中完全分裂.这包括重量一的形式，并有应用推广Buzzard和泰勒的主要定理。其次，我们遵循Kassaei的思想，将科尔曼的著名结果"小斜率的过收敛上特征形是经典的“推广到岩堀水平的p-adic过收敛Hilbert特征形的情况。
Abstract We generalise results of Buzzard, Taylor and Kassaei on analytic continuation of p-adic overconvergent eigenforms over ℚ to the case of p-adic overconvergent Hilbert eigenforms over totally real fields F, under the assumption that p splits completely in F. This includes weight-one forms and has applications to generalisations of Buzzard and Taylor’s main theorem. Next, we follow an idea of Kassaei’s to generalise Coleman’s well-known result that ‘an overconvergent Up-eigenform of small slope is classical’ to the case of p-adic overconvergent Hilbert eigenforms of Iwahori level.