Hecke eigenspaces for the projective line

Autor(es)

Alvarenga, Roberto ; Bonnel, Nans

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF NUMBER THEORY; v. 264, p. 40-pg., 2024-07-02.

Resumo

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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU)

• Processo FAPESP: 22/09476-7 - Formas automórficas para PGL_n
• Beneficiário: Roberto Carlos Alvarenga da Silva Junior
• Modalidade de apoio: Auxílio à Pesquisa - Regular