Work

Modular forms for $${{\,\textrm{GL}\,}}(r, \mathbb {F}_{q}[T])$$: $$t$$-expansions of the basic forms

Year: 2026

Type: article

Abstract: We give closed formulas for the first few expansion coefficients of the basic modular forms for $${{\,\textrm{GL}\,}}(r, \mathbb {F}_{q}[T])$$ GL ( r , F q [ T ] ) . Here the rank $$r$$ r is larger or equal to $$3$$ 3 , and the forms in question include the coefficient forms $$g_{1}, \dots , g_{r}$$ g 1 , ⋯ , g r and the Eisenstein series $$E_{q^{i}-1}$$ E q i - 1 ( $$i \in \mathbb {N}$$ i ∈ N ).

Source: The Ramanujan Journal

DOI: 10.1007/s11139-026-01359-9

Author: Ernst-Ulrich Gekeler

Institution: Saarland University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Universität des Saarlandes