A N A L Y T I C      N U M B E R    T H E O R Y ,     2 0 2 2

Lectures: Tuesday, Thursday, 2:00pm-3:15pm, in Warren Weaver Hall 512.

Lecturer: Paul Bourgade, office hours Friday 9.30-10.30am, you also can email me (bourgade@cims.nyu.edu) to set up an appointment or just drop by (WWH 603).

Course assistant: Sujay Kazi (ssk9840@nyu.edu). Sections: Friday 12.30-1.45pm, 194M 304.

Course description: An introduction to analytic methods in number theory. Some goals are the proof of Prime Number Theorem using the Riemann zeta function, Dirichlet’s theorem on prime numbers in an arithmetic progression, sieve methods. Mathematical technique is developed as needed. This includes basics of complex function theory and integration, Fourier analysis, and finite abelian groups (for Dirichlet’s theorem).

Prerequisites: Students must have Analysis I or specific permission of the instructor. Each of these is helpful but not required: Algebra I, Theory of Numbers, Complex Variables.

Textbooks: Our reference text will be The Distribution of Prime Numbers, by Dimitris Koukoulopoulos. An online version can be found here.

Homework: Every Thursday for the next Thursday.

Grading: problem sets (50%) and final (50%).

A tentative schedule for this course is:

Problem sets.