Selberg's sieve
Dr. Kai Man Tsang
The
Selberg's
L^{2}sieve is a neat and
versatile tool in analytic number theory.
Its main idea originates from Selberg's work on the theory of the
Riemann zetafunction back in the 1940's. Earlier applications of the L^{2}sieve include
approximations to the Goldbach and prime twins problems.
Since
2004, there are two extraordinary breakthroughs in the theory of the primes,
namely, the GreenTao theorem on arbitrarily long arithmetic progressions of
primes, and the GoldstonPintzYildirim theorems on small gaps between primes.
Selberg's L^{2}sieve played a central role in
both of these.
In
these two talks, I will first introduce the L^{2}sieve and describe
some of its earlier applications. Then I will discuss some more recent results
and describe the action of the L^{2}sieve in the abovementioned
breakthroughs in the distribution of the primes.
Lecture 1: 


Lecture 2: 
March 10, 2006
(Friday) 

Lectures will be held in Room 517, Meng Wah Complex,
HKU
Tea will
be held in Room 516, Meng Wah Complex at
All are welcome