Artin's Primitive Root Conjecture – A Survey
Copyright policy )Artin's Primitive Root Conjecture – A Survey
Abstract.One of the first concepts one meets in elementary number theory is that of the multiplicative order. We give a survey of the literature on this topic emphasizing the Artin primitive root conjecture (1927). The first part of the survey is intended for a rather general audience and rather colloquial, whereas the second part is intended for number theorists and ends with several open problems. The contributions in the survey on `elliptic Artin' are due to Alina Cojocaru. Wojciec Gajda wrote a section on `Artin for K-theory of number fields,' and Hester Graves (together with me) on `Artin's conjecture and Euclidean domains.'
- Max Planck Society Germany
Mathematics - Number Theory, Euclidean rings, Research exposition (monographs, survey articles) pertaining to number theory, Density, gaps, topology, number fields, 11R45, 11A07, elliptic curves, FOS: Mathematics, Asymptotic results on arithmetic functions, density of primes, Congruences; primitive roots; residue systems, primitive root, Number Theory (math.NT), Artin's conjecture
Mathematics - Number Theory, Euclidean rings, Research exposition (monographs, survey articles) pertaining to number theory, Density, gaps, topology, number fields, 11R45, 11A07, elliptic curves, FOS: Mathematics, Asymptotic results on arithmetic functions, density of primes, Congruences; primitive roots; residue systems, primitive root, Number Theory (math.NT), Artin's conjecture
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