Jump to ContentJump to Main Navigation
Show Summary Details

Artin's Primitive Root Conjecture – A Survey

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


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.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Francesco Pappalardi and Andrea Susa
Archiv der Mathematik, 2013, Volume 101, Number 4, Page 319
Nati Linial, Ilan Newman, Yuval Peled, and Yuri Rabinovich
Israel Journal of Mathematics, 2018
Edward Tremel, Ken Birman, Robert Kleinberg, and Márk Jelasity
ACM Transactions on Cyber-Physical Systems, 2018, Volume 3, Number 2, Page 1
M. Ram Murty, François Séguin, and Cameron L. Stewart
Journal of Number Theory, 2018
Bulletin of the Australian Mathematical Society, 2017, Page 1
Christian Borst, Evan Boyd, Claire Brekken, Samantha Solberg, Melanie Matchett Wood, and Philip Matchett Wood
Experimental Mathematics, 2017, Page 1
Cihan Pehlivan
International Journal of Number Theory, 2016, Volume 12, Number 08, Page 2147
Christophe Debry and Antonella Perucca
Journal of Number Theory, 2016, Volume 167, Page 259
Antonella Perucca
Journal of Number Theory, 2015, Volume 148, Page 121
Paul Pollack
Algebra & Number Theory, 2014, Volume 8, Number 7, Page 1769

Comments (0)

Please log in or register to comment.
Log in