On Artin's Conjecture for Rank One Drinfeld Modules

Chih Nung Hsu*, Jing Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Let k be a global function field with a chosen degree one prime divisor ∞, and O⊂k is the subring consisting of all functions regular away from ∞. Let φ be a sgn-normalized rank one Drinfeld O-module defined over O′, the integral closure of O in the Hilbert class field of O. We prove an analogue of the classical Artin's primitive roots conjecture for φ. Given any a≠0 in O′, we show that the density of the set consisting of all prime ideals P′ in O′ such that a (modP′) is a generator of φ(O′/P′) is always positive, provided the constant field of k has more than two elements.

Original languageEnglish
Pages (from-to)157-174
Number of pages18
JournalJournal of Number Theory
Issue number1
Publication statusPublished - 2001 May


  • Artin's conjecture; Drinfeld modules; function fields

ASJC Scopus subject areas

  • Algebra and Number Theory


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