We use the gluing construction introduced by Jia Huang to explore rings of invariants for a range modular representations. construct generating sets maximal parabolic subgroups finite symplectic group and their common Sylow p -subgroup. also investigate singular classical groups. introduce this compute invariant field fractions thin faithful representations semidirect products determine minimum...

∈ Γ let ||γ|| = max(|a|, |b|, |c|, |d|). In this paper we show that for given f the modular symbol as logarithmic growth, i.e., | 〈γ, f〉 | ≤ A log ||γ||+B for some A,B ≥ 0. In [2, 3], D. Goldfeld conjectured that the modular symbol has moderate growth if also f is allowed to vary among the normalized newforms. The result of the present paper reduces Goldfeld’s conjecture to a statement on the g...