Hecke eigenspaces for the projective line

Pub Date : 2024-06-26 DOI:10.1016/j.jnt.2024.05.010
Roberto Alvarenga , Nans Bonnel
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Abstract

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 Fq and for the group GL2. 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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投影线的赫克特征空间
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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