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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Analogues of Artin's conjecture


Author: Larry Joel Goldstein
Journal: Trans. Amer. Math. Soc. 149 (1970), 431-442
MSC: Primary 10.65
DOI: https://doi.org/10.1090/S0002-9947-1970-0279066-3
MathSciNet review: 0279066
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Abstract: Based on heuristic, a general conjecture is made, which contains Artin's primitive root conjecture as a special case. Special cases of the general conjecture are verified using the generalized Siegel-Walfisz theorem. It is shown that the general conjecture can be considered as an infinite-dimensional analogue of the Tchebotarev density theorem.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0279066-3
Keywords: Number field, zeta function, Riemann hypothesis, primitive root, density of primes, Tchebotarev's theorem, locally compact group, Haar measure, equidistribution
Article copyright: © Copyright 1970 American Mathematical Society