A remark on non-integral p-adic slopes for modular forms
A remark on non-integral p-adic slopes for modular forms
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关于模形式的非积分 p-adic 斜率的评论
DOI：
10.1016/j.crma.2017.01.012
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发表时间：
2017
影响因子：
0.8
通讯作者：
Pollack, Robert
中科院分区：
文献类型：
--
作者：
Bergdall, John;Pollack, Robert
Tp作用于Sk（0（N））。本文的作者还提出了一个单独的猜想（[3]），它预言了驯服level 0（N）的所有p-adic模形式的Up-slope，仍然假设p是0（N）-正则的。这两种理论在实验上是一致的，但还没有被证明是一致的。Buzzard的猜想清楚地表明，每个斜率都是整数。(This[3]中的含义根本不清楚。斜坡的完整性是否具有0（N）-正则性的特征是一个值得探讨的问题。我们证明它是。证明占据了第二部分。
Tp acting on Sk (0 (N)). The authors of the present work also have made a separate conjecture ([3]) which predicts the U p-slopes of all p-adic modular forms of tame level 0 (N) still assuming that p is 0 (N)-regular. The two conjectures are consistent with each other experimentally, but have not yet been shown to be consistent in general. Buzzard’s conjecture clearly implies that every slope is an integer.(This implication is not at all clear from the conjectures in [3].) It is worth asking if the integrality of slopes is characteristic of 0 (N)-regularity. We show that it is. The proof occupies the second section.