Leon Takhtajan

Department of Mathematics
Stony Brook University

office: Math Tower 5-111
phone: (631) 632-8287
e-mail: leon.takhtajan@stonybrook.edu

MAT 401 Seminar in Mathematics: Analytic Number Theory
Fall 2021

Course description

The goal of the seminar is to introduce the students to powerful analytic methods in number theory. We will cover the following three major topics:

If time permits, we will also discuss Dirichlet L-series, distribution of prime numbers in arithmetic progressions and the Bombieri-Vinogradov theorem.

I will give a few short lectures on each topic and will assign further material for the students to read and to present in class. Corresponding topics and reading material will be regularly posted on the Blackboard.

We will be using the following classic books:
  • K. Chandrasekharan Introduction to Analytic Number Theory, Springer; softcover reprint of the original 1968 edition (March 1, 2012)

  • H.M. Edwards, Riemann's Zeta Function, Dover edition, 2001.

  • S.J. Patterson, An Introduction to the Theory of the Riemann Zeta-Function, Cambridge University Press, 1995.

  • J.-P. Serre A Course in Arithmetics, Springer, 1996.

  • Measurable Learning Outcomes

    Upon successful completion of MAT 401 Seminar in Mathematics: Analytic Number Theory, a student will:
  • Be familiar with the contributions of great mathematicians of the past.

  • Be conversant with the specialized vocabulary of the topic of analytic number theory.

  • Be ablie to rigorously prove the main results specific to the topic.

  • Be able to solve routine problems and quote assumptions and main theorems of the topic.

  • Appreciate the relationship of the topic to the undergraduate mathematics curriculum.

  • Lectures

    Tuesday and Thursday 1:15pm-2:35pm in Earth & Space 177.


    Leon Takhtajan

    Office hours: Wednesday, 2:00pm-4:00pm in Math Tower 5-111, and by appointment, in person or by zoom.


    There is no formal textbook required to this class. Instead, it is required that to read, on a regular basis, all materials posted in the Blackboard.


    Students need to have completed MAT342 and MAT312 or 313; completion of MAT311 is also recommended.

    Grading Policy

    The grades will be based on the class participation, the oral presentations and on solution of selected homework problems.

    Student Accessibility Support Center Statement

    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities and search Fire Safety and Evacuation and Disabilities.

    Academic integrity

    Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html.

    Critical Incident Management

    Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Until/unless the latest COVID guidance is explicitly amended by SBU, during Fall 2021 "disruptive behavior” will include refusal to wear a mask during classes.

    Last updated January 2021