18.785: Analytic Number Theory, MIT, spring 2007 (K.S. Kedlaya)
The prime number theorem
Most of my handouts will come with exercises attached; see the web site for the due dates. (For example, these are due February 14.) There are likely to be typos in
18.785: Analytic Number Theory, MIT, spring 2007 (K.S. Kedlaya)
Dirichlet characters and Dirichlet L-series
In this unit, we introduce some special multiplicative functions, the Dirichlet characters,
and study their corresponding Dirichlet series. We will
18.785: Analytic Number Theory, MIT, spring 2006 (K.S. Kedlaya)
Introduction to the course
Welcome to 18.785! This course is meant to be an introduction to analytic number
theory; this handout provides an overview of what we will be talking about in the c
18.785: Analytic Number Theory, MIT, spring 2006 (K.S. Kedlaya)
Dirichlet series and arithmetic functions
1
Dirichlet series
The Riemann zeta function is a special example of a type of series we will be considering
often in this course. A Dirichlet series
18.785: Analytic Number Theory, MIT, spring 2007 (K.S. Kedlaya)
Primes in arithmetic progressions
In this unit, we rst prove Dirichlets theorem on primes in arithmetic progressions. We
then prove the prime number theorem in arithmetic progressions, modulo