投影线的赫克特征空间

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-06-26 DOI:10.1016/j.jnt.2024.05.010

Roberto Alvarenga , Nans Bonnel

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引用次数: 0

摘要

在这篇文章中，我们研究了（有夯和无夯）赫克算子对投影线的函数域的自变形式的作用，该函数域定义在...上，并为...群。我们首先计算未ramified Hecke 代数中每个生成器的 Hecke 特征空间维数。因此，我们考虑了阶数为 1 的点的斜切，并明确描述了某些斜切赫克算子对自动形式的作用。此外，我们还计算了这些夯化赫可算子的特征空间维数。文章的最后，我们考虑了更一般的斜切，即那些与更高阶的闭合点相连的斜切。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hecke eigenspaces for the projective line

In this article we investigate the action of (ramified and unramified) Hecke operators on automorphic forms for the function field of the projective line defined over $F_{q}$ and for the group ${GL}_{2}$ . We first compute the dimension of the Hecke eigenspaces for every generator of the unramified Hecke algebra. Thus, we consider the ramification in a point of degree one and explicitly describe the action of certain ramified Hecke operators on automorphic forms. Moreover, we also compute the dimensions of its eigenspaces for those ramified Hecke operators. We finish the article considering more general ramifications, namely those one attached to a closed point of higher degree.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.