Description
Prime numbers have fascinated humans for millennia, and one of their cardinal mysteries is their irregular distribution on the number line. One of the great theorems is mathematics is the Prime Number Theorem, which gives an asymptotic estimate for the number of primes less than a given bound. A simple yet detailed proof of the Prime Number Theorem is the capstone goal of this course.
For a detailed investigation on prime numbers, we will need to build up some tools. The main objects of study in this course are functions of number-theoretic origin, i.e. arithmetic functions. A good deal of the course will be spent building up techniques for estimating sums of arithmetic functions and showing their equivalence with Dirichlet series. The latter allows us to bring to bear powerful techniques from real and complex analysis on the study of arithmetic functions. These tools will lead us to clear proofs of Dirichlet's theorem on primes in arithmetic progressions and the Prime Number Theorem.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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