Artin's primitive root conjecture for function fields revisited |
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| Affiliation: | 1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, 9000 Gent, Flanders, Belgium;2. Department of Mathematics and Data Science, University of Brussels (VUB), Pleinlaan 2, Building G, 1050 Elsene, Brussels, Belgium;3. Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia |
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| Abstract: | Artin's primitive root conjecture for function fields was proved by Bilharz in his thesis in 1937, conditionally on the proof of the Riemann hypothesis for function fields over finite fields, which was proved later by Weil in 1948. In this paper, we provide a simple proof of Artin's primitive root conjecture for function fields which does not use the Riemann hypothesis for function fields but rather modifies the classical argument of Hadamard and de la Vallée Poussin in their 1896 proof of the prime number theorem. |
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| Keywords: | Artin's conjecture Function fields Finite fields |
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