The Prime Number Theorem Jameson Pdf 21

Also I'll put up notes on this website. My aim in this course will be to discuss several problems related to the distribution of prime numbers. One high point for the course will be the proof of the prime number theorem which gives an asymptotic for the number of primes up to x. I will also discuss Riemann's seminal paper introducing the zeta function as a tool in prime number theory, explain some of the properties of zeta, and the connection between primes and the Riemann hypothesis. Other topics may include sieves (e.g. showing upper bounds for the number of twin primes), the primality test, gaps between primes etc. I will assume that you have some knowledge of number theory already, at the level of 152, and that you're also comfortable with analysis and thinking about the size of things, and have some familiarity with complex analysis (say, up to Cauchy's theorem). If you're concerned with the background, please feel free to talk to me. To brush up on complex analysis you could look at the book by Green and Krantz (Function theory of one complex variable, first four chapters), or Ahlfors (Complex Analysis, first four chapters), or Copson (An introduction to the theory of functions of a complex variable, first six chapters). 2b1af7f3a8