Analytic Number Theory: MATH6110
Important Information :
I will hold special office hours on Thursday June 23 from 1:00 pm to 2:30 pm in my office Ross N515.
The final (comprehensive) exam will be held on Tuesday June 28, 2016 from 11:30 am to 2:30 pm in N501 Ross.
Instructor: Dr. Youness Lamzouri.
Office: N515 Ross Building.
Time and location : Tuesdays and Thursdays, 11:30 am--2:30 pm, in Ross S156.
Office hours: Tuesdays 3:30--4:30 pm or by appointment.
Text for the course: The course will be based primarily on lecture notes. Parts of the notes of A. J. Hildebrand will serve as a useful reference. Other important references include the following texts:
H. L. Montgomery and R. C. Vaughan, "Multiplicative Number Theory I: Classical Theory". Cambridge University Press (2007).
H. Davenport, "Multiplicative Number Theory". Graduate Texts in Mathematics, Springer (2000).
Important Announcement: There will be no class during the week of May 16-20. Make-up classes will be scheduled on June 3 and June 17 from 2:00 to 5:00 pm in Ross N501.
Course Description :
This course will provide an introduction to analytic number theory, the branch of modern number theory that uses real and complex analysis to study the distribution of arithmetic objects, especially the prime numbers. Covered topics include: mean values of arithmetic functions, the prime number estimates of Chebyshev and of Mertens, Dirichlet series and Euler products, the theory of the Riemann zeta function, Dirichlet characters and Dirichlet $L$-functions, the proof of the prime number theorem, the distribution of prime numbers in arithmetic progressions.