Olivier Ramaré

This talk will retrace the main steps of the modern theory of prime numbers and in particular how the combinatorial sieve combined with the Dirichlet series theory to give birth to the modern representation of the primes via a linear combination of...

Dirichlet polynomials do not take large values at close-by points. The theory of large values of Dirichlet polynomials introduced by Montgomery in 1969 elaborates on this idea. We will present the large sieve argument of Montgomery, the dissection...

If the average behaviour of the prime numbers is well known, the local one is much more mysterious, and many questions are not even amenable (as of today) to heuristics! We will address three questions: what is the largest number of primes in a given...

Motohashi (following Selberg) developped in 1978 a method to prove the Hoheisel and Linnik theorem without any deep mention of the zeros. We will present this approach. The first lecture will be a sketch of the argument and will introduce the tools...

Motohashi (following Selberg) developped in 1978 a method to prove the Hoheisel and Linnik theorem without any deep mention of the zeros. We will present this approach. The first lecture will be a sketch of the argument and will introduce the tools...

We will present a surprising exact and truncated Perron summation formula as well as several other formulaes. We will proceed by comparing the relative strenghts of the smoothing method versus Perron summation.

The last years have seen the proof of many results concerning the prime numbers. We will show how these results are all related to linear equations with prime indeterminates, and from then on, recount the history of the quantitative version of the...

This talk will retrace the main steps of the modern theory of prime numbers and in particular how the combinatorial sieve combined with the Dirichlet series theory to give birth to the modern representation of the primes via a linear combination of...