Analytic Number Theory: MATH6110

Summer 2016

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.

  • General Information:

  • 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.

    Course Evaluation:

  • 60% Assignments : Assignments will be given every two weeks. In total, there will be three assignments counting for 20% each. For each assignment, a random selection of questions will be chosen for grading. Late assignments will not be accepted except in the event of illness (with supporting medical documentation), or with prior consent of the instructor.

    Assignment 1 (Due Thursday May 26, 2016 at the beginning of class).

    Assignment 2 (Due Thursday June 9, 2016 at the beginning of class).

    Assignment 3 (Due Tuesday June 28, 2016).

  • 40% Final Exam: The final exam will be comprehensive.