On primitive roots for rank one Drinfeld modules |
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| Authors: | Wei-Chen Yao Jing Yu |
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| Institution: | a Department of Mathematics and Computer Science Education, Taipei Municipal University of Education, No. 1, Aikuo West Road, Taipei, 10048, Taiwan, ROC
b Department of Mathematics, National Taiwan University, Taipei, Taiwan, ROC |
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| Abstract: | Let k be a global function field over a finite field and let A be the ring of the elements in k regular outside a fixed place ∞. Let K be a global A-field of finite A-characteristic and let ? be a rank one Drinfeld A-module over K. Given any α∈K, we show that the set of places P of K for which α is a primitive root modulo P under the action of ? possesses a Dirichlet density. We also give conditions for this density to be positive. |
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| Keywords: | 11T55 |
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