Arithmetic properties of Fredholm series for p‐adic modular forms
Arithmetic properties of Fredholm series for p‐adic modular forms
复制标题
p-adic 模形式的 Fredholm 级数的算术性质
DOI：
10.1112/plms/pdw031
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发表时间：
2015
影响因子：
1.8
通讯作者：
R. Pollack
中科院分区：
文献类型：
--
作者：
John Bergdall;R. Pollack
我们研究了在p-进权空间的“边界附近”的过收敛p-进模形式的斜率上的最近构造之间的关系。我们还证明了在驯服的水平1，系数的Fredholm系列的向上运营商永远不会消失模p，一种现象，失败在更高的水平。在更高层次上，我们使用Andreatta，Iovita和Pilloni最近发现的Fredholm级数的mod p约化的模解释来检查无穷多个系数是非零模p。
We study the relationship between recent conjectures on slopes of overconvergent p ‐adic modular forms ‘near the boundary’ of p ‐adic weight space. We also prove in tame level 1 that the coefficients of the Fredholm series of the Up operator never vanish modulo p , a phenomenon that fails at higher level. In higher level, we do check that infinitely many coefficients are non‐zero modulo p using a modular interpretation of the mod p reduction of the Fredholm series recently discovered by Andreatta, Iovita and Pilloni.