Sieve methods

Sieve methods are an important part of analytic number theory that give access to a host of questions around the representation of prime numbers by (systems of) polynomials, and beyond.
In this course, assuming very little of the reader, we shall cover some of the basic introductory material on sieve theory, building up to a full account of the most important upper bound sieves: the large sieve and the Selberg sieve. We shall discuss some of the limitations of sieve methods and, if time permits, the famous recent work of Maynard on bounded gaps between primes.

Target group: Anyone interested in prime number theory and Diophantine equations.

Prerequisites: Some prior familiarity with analytic number theory would be useful.

Evaluation: Performance on exercise sheets

Teaching format: Lectures with exercise classes

ECTS: 3 Year: 2021

Track segment(s):
MAT-ANA Mathematics - Analysis
MAT-DISC Mathematics - Discrete Mathematics

Teacher(s):
Timothy Browning

Teaching assistant(s):

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