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This research explores the transcendence of special values of Goss L-functions for Drinfeld modules in finite fields.

December 11, 2025

On the transcendence of special values of Goss L -functions attached to Drinfeld modules

Key Points

This research explores the transcendence of special values of Goss L-functions for Drinfeld modules in finite fields.
Analyzed Goss L-functions associated with Drinfeld modules defined over finite fields.
Studied special values of Goss L-functions in the context of abelian motives.
Investigated Drinfeld modules of rank with good reduction.
Established transcendence of specific Goss L-function values over finite fields.
Proved that values at positive integers from the exterior power of Drinfeld modules are transcendental.

Abstract

Let Formula: see text be the finite field with Formula: see text elements and consider the rational function field Formula: see text. For a Drinfeld module Formula: see text defined over Formula: see text, we study the transcendence of special values of the Goss Formula: see text-function attached to the abelian Formula: see text-motive Formula: see text of Formula: see text. Moreover, when Formula: see text is a Drinfeld module of rank Formula: see text defined over Formula: see text which has everywhere good reduction, we prove that the value of the Goss Formula: see text-function attached to the Formula: see text-st exterior power of Formula: see text at any positive integer is transcendental over Formula: see text.

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