MATH 843, Analytic Number Theory

• Elementary Number Theory - Hopefully you all know this already
• Distribution of Prime Numbers

For basics about continued fractions, see for instance Lecture Notes for sessions 20, 21, 22, 23 from:

Kumar, Abhinav. 18.781 Theory of Numbers,Spring 2012. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 26 Feb, 2013). License: Creative Commons BY-NC-SA

For the part about Diophantine approximation we largely follow the notes from Beukers and Evertse for their Master course Diophantine Equations, 2011, in particular

• Notes on Diophantine Equations for an intro to Thue Equations and Skolem's method
• Notes on the Siegel-Mahler Theorem for S-unit equations
• Notes on Linear forms in Logarithms for Baker's effective results.

Further literature references:

• Harold Davenport, Multiplicative Number Theory, GTM 74, Springer (1980).
• Tom M. Apostol, Introduction to analytic number theory, UTM, Springer (1976).
• Hugh Montgomery and Robert Vaughan, Multiplicative Number Theory I. Classical Theory, CSAM 97, Cambridge University Press (2007).

Online notes

• Notes by Noam Elkies for Harvard MATH 259. Does things in a little bit different order but his notes are very high in motivation, so make for a nice background reading.
• Notes by Ben Green