# Tensor powers of rank 1 Drinfeld modules and periods

## TL;DR

This paper investigates tensor powers of rank 1 Drinfeld modules over elliptic curves, deriving explicit formulas for their A-action and period lattices using A-motives and Anderson generating functions.

## Contribution

It introduces explicit formulas for the A-action and period lattices of tensor powers of rank 1 Drinfeld modules, advancing the understanding of their structure.

## Key findings

- Explicit formulas for A-action of tensor powers
- Development of vector-valued Anderson generating functions
- Descriptions of period lattices for these modules

## Abstract

We study tensor powers of rank 1 sign-normalized Drinfeld A-modules, where A is the coordinate ring of an elliptic curve over a finite field. Using the theory of A-motives, we find explicit formulas for the A-action of these modules. Then, by developing the theory of vector-valued Anderson generating functions, we give formulas for the period lattice of the associated exponential function.