Analytic Number Theory

October - December 2007.  Dr. Tim Browning.

Part A (Lectures 1-10):  Basic topics in Analytic Number Theory.

• Arithmetic functions and Dirichlet series.
• Riemann zeta function.
• Prime number theorem.

Reading (among many possible sources):

• T. M. Apostol, Introduction to analytic number theory. Springer, 1976.
• H. Davenport, Multiplicative number theory, 3rd ed., Springer 2000.
• H. Iwaniec and E. Kowalski, Analytic number theory, AMS 2004.

Part B (Lectures 11-20):  Advanced topics in Analytic Number Theory I.

• Overview of Diophantine equations.
• The Hardy-Littlewood Circle Method.
• Application to diagonal forms.

Reading (among many possible sources):

• H. Davenport, Analytic methods for Diophantine equations and Diophantine inequalities, 2nd ed., CUP, 2005.

Course Notes:

Sean Prendiville has very kindly typeset the lecture notes for the first half of the course.

• Part A lecture notes

Course Assessment:

The course will be assessed by problem sheets that will be assigned during the lectures.

• Problem sheet A
• Problem sheet B

Please send your attempts to Tim Browning, School of Mathematics, University of Bristol, Bristol, BS8 1TW.