2023/08/17 by Roberto Alvarenga, Alvarenga, Roberto, Nans Bonnel +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2308.08720
openalex publication_date 2023/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a finite field 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 describe explicitly the action of certain ramified Hecke operators on automorphic forms. Moreover, for those ramified Hecke operators, we also compute the dimensions of its eigenspaces. We finish the article considering more general ramifications, namely, those one attached to a closed point of higher degree.