Artin's conjecture on average and short character sums
Event details
| Date | 25.11.2025 |
| Hour | 14:15 › 16:00 |
| Speaker | Igor Shparlinski (UNSW Sydney) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Let N_a(x) denote the number of primes up to x for which the integer a is a primitive root. We show that N_a(x) satisfies the asymptotic predicted by Artin's conjecture for almost all
1\le a\le exp((log log x)^2). This improves on a result of Stephens (1969) which applies to the much longer range 1 \le a \le exp(6(log x log log x)^{1/2} )). 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).
Joint work with Oleksiy Klurman and Joni Teräväinen.
Practical information
- Informed public
- Free
Contact
- Juliana Velasquez