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Artin's conjecture for
Drinfeld modules
Wentang Kuo and David Tweedle |
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Vol. 16 (2022), No. 5, 1025–1070
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Abstract |
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Let be a Drinfeld module of rank with generic characteristic, and suppose that the endomorphism ring of induces a Drinfeld module of rank . Let . We prove that the set of places of for which generates as an -module has a density. Furthermore, we show that this density is positive other than in some standard exceptional cases. We also revisit Artin’s problem for Drinfeld modules of rank , first considered by Hsu and Yu. A key point is that our methods do not require that be a principal ideal domain. We are also able to generalize a Brun–Titchmarsh theorem for function fields proved by Hsu. |
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Keywords
Artin's primitive root conjecture, function fields,
Drinfeld modules
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Mathematical Subject Classification 2010
Primary: 11G09
Secondary: 11G15, 11R45
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Milestones
Received: 22 February 2020
Revised: 13 April 2021
Accepted: 22 August 2021
Published: 16 August 2022
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Authors |
| Wentang Kuo | |
| Department of Pure Mathematics University of Waterloo Waterloo ON Canada |
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| David Tweedle | |
| Department of Mathematics and
Statistics The University of the West Indies, St. Augustine Campus St. Augustine Trinidad and Tobago |
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