A family of Hecke eigenforms for Drinfeld modular forms of arbitrary rank

2025/09/25 by Gezmiş, Oğuz, Ülkem, Özge
#11F52 (Primary) #11G09 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.20895

Abstract

We aim to provide a family of Drinfeld-Hecke eigenforms given in terms of a determinant of twisted Eisenstein series. Our main tool is the theory of vectorial Drinfeld modular forms, previously introduced by Pellarin [18] and extensively studied by Pellarin [19] as well as in his joint work with Perkins [20] in the rank two setting. We will develop this theory in the present paper for the arbitrary rank setting by using a particular representation.

Citations

• Hecke operators for higher rank Drinfeld modular forms
• On the partial derivatives of Drinfeld modular forms of arbitrary rank
• Effective rigid analytic trivializations for Drinfeld modules
• On Drinfeld modular forms of higher rank and quasi-periodic functions
• The analytic theory of vectorial Drinfeld modular forms
• Compactification of Drinfeld modular varieties and Drinfeld Modular Forms of Arbitrary Rank

Related

• Drinfeld modular forms of arbitrary rank, Part III: Examples
• Twisting eigensystems of Drinfeld Hecke eigenforms by characters
• Drinfeld Quasi-Modular Forms of Higher Level
• Hecke operators for higher rank Drinfeld modular forms
• Drinfeld modular forms of arbitrary rank, Part I: Analytic Theory