Teaching


Spring 2020

In the Spring semester 2020, I will be teaching MATH-GA 2210.001 Introduction to Number Theory I.

Attention: following NYU-wide policy, classes will meet remotely starting Wednesday, March 11th. If you are registered for this class, you can access the online meeting tool Zoom via NYU Classes. If not, you can e-mail me and I will add you to the meeting manually.

Lectures:

W 5:10-7pm in CIWW 1302.

Contact information:

Office 604
bilu @ cims.nyu.edu (remove blank spaces around @)

Office hours:

W4-5pm, or by appointment. While NYU is functioning remotely, please e-mail me to set up a meeting via Zoom if you have questions.

Contents of the course:

This is a course in Number Theory, covering mostly analytic aspects. Topics include: primes in arithmetic progressions, zeta function, prime number theorem, circle method.

Recommended books

I do not require a textbook for this course, and will partly follow Prof. Pirutka's notes from a few years ago, available here, as well as Kiran Kedlaya's notes, available here. Other good references include:
  1. A. Karatsuba, Basic Analytic Number Theory
  2. K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory
  3. S. Miller, R. Takloo-Bighash, An Invitation to Modern Number Theory
  4. H. Edwards, Riemann's Zeta function
  5. T. Apostol, Introduction to Analytic Number Theory
  6. M. Ram Murty, Problems in Analytic Number Theory
  7. G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory

Most of these books can be accessed online via the NYU library catalog.

Lecture notes

Here are some lecture notes to help you follow the course while NYU is functioning remotely:
March 11th
March 25th
Videos of lectures in April-May and corresponding lecture notes are also available, contact me if you want access.

Homeworks:

Homeworks are always due in the beginning of Wednesday's class, unless otherwise announced. If you cannot attend class, you can e-mail me your homework before the beginning of class, or leave it in my mailbox (number 38 on the right side of the mailboxes behind the guard's desk in the lobby of WWH). Late homeworks are usually not accepted, except if you have a valid excuse, which you should e-mail me about in advance. Starting at Homework 6, assignments must be submitted as a single PDF file via NYU Classes. Frequency of homeworks will vary, check NYU Classes for exact due date.

Homework 1 (due February 12th): Introduction, Riemann zeta function
Homework 2 (due February 19th): Dirichlet characters and L-functions. Some hints/partial solutions
Homework 3 (due February 26th): Densities
Homework 4 (due March 4th): Gamma function
Homework 5 (due March 11th): Zeta function, functional equation
Homework 6 (due March 25th): Zero-free regions, contour integration
Homework 7 (due April 1st): Prime number theorem and further topics
Homework 8 (due April 10th): Further topics around zeta; special values
Homework 9 (due April 19th): Circle method
Homework 10 (due May 1st): Circle method: difference operators.

Older teaching:

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