# Explicit formulas and vanishing conditions for certain coefficients of Drinfeld-Goss Hecke eigenforms

## TL;DR

This paper derives explicit formulas for specific coefficients of Drinfeld-Goss Hecke eigenforms and uses these formulas to establish vanishing conditions for an infinite family of coefficients, advancing understanding of their structure.

## Contribution

It provides a closed form polynomial expression for coefficients of Drinfeld-Goss eigenforms and proves their vanishing under certain conditions, which is a novel analytical development.

## Key findings

- Explicit polynomial formulas for coefficients of Drinfeld-Goss eigenforms
- Proof of vanishing conditions for an infinite family of coefficients
- Enhanced understanding of the structure of Drinfeld-Goss modular forms

## Abstract

We obtain a closed form polynomial expression for certain coefficients of Drinfeld-Goss double-cuspidal modular forms which are eigenforms for the degree one Hecke operators with power eigenvalues, and we use those formulas to prove vanishing results for an infinite family of those coefficients.