On Artin's conjecture on average and short character sums
Abstract Let denote the number of primes up to for which the integer is a primitive root. We show that satisfies the asymptotic predicted by Artin's conjecture for almost all . This improves on a result of Stephens (1969). A key ingredient in the proof is a new short character sum estimate over the integers, improving on the range of a result of Garaev (2006).
Authors
- Joni Teräväinen (ORCID: https://orcid.org/0000-0001-6258-8004)
- Igor E. Shparlinski (ORCID: https://orcid.org/0000-0002-5246-9391)
- Oleksiy Klurman
Institutions
- University of Turku (FI)
- UNSW Sydney (AU)
- University of Bristol (GB)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2025-05-23
- DOI
- https://doi.org/10.1112/blms.70103
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Academy of Finland
- Australian Research Council