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Integers


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Artin's Primitive Root Conjecture – A Survey

Pieter Moree
Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0043

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.'

Keywords: Multiplicative Order; Primitive Root; Density; Number Field; Euclidean Ring; Elliptic Curve

About the article

Received: 2011-06-07

Revised: 2012-06-29

Accepted: 2012-07-27

Published Online: 2012-11-30

Published in Print: 2012-12-01


Citation Information: Integers, Volume 12, Issue 6, Pages 1305–1416, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0043.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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