Abstract / résuméCUMC / CCEM 2005

Name / nom: Eugene Eisenstein

School / école: University of Waterloo

Length / durée: 50 min

Title / titre: Applications of Sieving Techniques in Not-so-basic Number Theory

Abstract / résumé: Many people are familiar with the grade-school form of the Sieve of Eratosthenes. This simple looking algorithm for finding prime numbers can be refined through clever tricks to yield a very powerful theorem in analytic number theory. This theorem, as we will see, can be used to answer questions about such hot topics as the twin prime conjecture. Not only that, it sparks the ideas for several other counting techniques, one of which is called Selberg's Sieve. We will discuss this sieve as well, and see some applications of it to a conjecture on elliptic curves that is important for cryptography.

Prerequisites / choses nécessaires: I will avoid the use of anything sophisticated. A course in analytic number theory will be beneficial. Anyone comfortable with higher mathematics should be able to follow my presentation.



PDF format / format PDF: eisenstein.pdf