Thursday October 29th, 2020 | |
| Time: | 4:30 PM - 5:30 PM |
| Title: | Primes in arithmetic progressions: The Riemann Hypothesis - and beyond! |
| Speaker: | James Maynard, Oxford University |
| Abstract: | |
| One of the oldest problems about prime numbers is asking how many primes there are of a given size in an arithmetic progression. Dirichlet's famous theorem shows that there are large primes in any progression unless there is an obvious reason why not, but more refined questions lead quickly to statements equivalent to versions of the Riemann Hypothesis, which unfortunately remains unsolved. We can prove that the Generalized Riemann Hypothesis is true 'on average', and this can often be used as an unconditional substitute for the Riemann Hypothesis. I'll introduce these ideas and mention some recent work about primes in arithemetic progressions which 'breaks the 1/2 barrier' and shows that something *stronger* that the Riemann Hypothesis holds on average. | |