#### Hall 123

#### An elementary approach to the distribution of primes in large arithmetic progressions

#### Olivier Ramare

##### CNRS / Institut de Mathematiques de Marseille

*Let X be some large parameter, and q be an integer of size about X^{1/2}. We will present a straightforward proof of the estimate*

sum_{p\le X} exp(2i Pi p/q) \ll X/(\log X)^100

due to I.M. Vinogradov in 1937 and comment on its meaning. Here p ranges through the primes.

Note:

1. This is an in-person seminar. Please follow all covid protocols.

2. Please note the change in date and time for the seminar due to the weather conditions.

Done