Hecke operators for higher rank Drinfeld modular forms

TL;DR

This paper investigates the action of Hecke operators on higher rank Drinfeld modular forms, providing explicit calculations, eigenvalues, and multiplicativity properties to advance understanding in this area.

Contribution

It introduces explicit calculations of Hecke operators on u-expansions and establishes the complete multiplicativity of a natural class of these operators.

Findings

Calculated the effect of simple Hecke operators on u-expansions.

Determined the eigenvalue for the Drinfeld discriminant function Δ_t.

Proved that a certain class of Hecke operators is completely multiplicative.

Abstract

We calculate the effect of simple Hecke operators on u-expansions of higher rank Drinfeld modular forms, the eigenvalue for the Drinfeld discriminant function $\Delta_t$ and show that a certain natural class of Hecke operators is completely multiplicative.