A Case Study on Hooley's Conditional Proof of Artin's Primitive Root Conjecture

Authors

Shalome Kurian, University of Warwick, CoventryFollow

Abstract

Artin’s Primitive Root Conjecture represents one of many famous problems in elementary number theory that has resisted complete solution thus far. Significant progress was made in 1967, when Christopher Hooley published a conditional proof of the conjecture under the assumption of a certain case of the Generalised Riemann Hypothesis. In this survey we present a description of the conjecture and the underlying algebraic theory, and provide a detailed account of Hooley’s proof which is intended to be accessible to those with only undergraduate level knowledge. We also discuss a result concerning the qx+1 problem, whose proof requires similar techniques to those used by Hooley.

Author Bio

Shalome Kurian is a fourth-year Mathematics undergraduate at the University of Warwick. He is most interested in pure mathematics and in particular number theory and analysis. During the summer of 2019 he completed a URSS project in which he wrote a survey paper on Artin's Primitive Root Conjecture. In his spare time, he enjoys playing tennis and similar sports.

Faculty Sponsor

Samuel Le Fourn

Recommended Citation

Kurian, Shalome (2020) "A Case Study on Hooley's Conditional Proof of Artin's Primitive Root Conjecture," Rose-Hulman Undergraduate Mathematics Journal: Vol. 21: Iss. 2, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss2/3