# Log-algebraic identities on Drinfeld modules and special L-values

## TL;DR

This paper proves a general log-algebraicity theorem for Drinfeld modules over polynomial rings, extending previous results, and demonstrates that certain special L-values are transcendental and expressible as linear forms in logarithms.

## Contribution

It generalizes Anderson's rank one log-algebraicity results to arbitrary rank Drinfeld modules and links special L-values to transcendental logarithmic forms.

## Key findings

- Log-algebraicity theorem for arbitrary rank Drinfeld modules
- Special L-values are linear forms in Drinfeld logarithms
- Certain L-values are transcendental

## Abstract

We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring F_q[theta]. This generalizes results of Anderson for the rank one case. As an application we show that certain special values of Goss L-functions are linear forms in Drinfeld logarithms and are transcendental.