Math 689 (Section 600) -- Fall 2019

Analytic theory of L-functions

Tuesday & Thursday 9:35-10:50
Location BLOC 624

Course Description:

This is a class on analytic properties of L-functions.   Topics we will cover this semester include
  • Definitions of L-functions
  • Constructions of L-functions (Dirichlet characters, modular forms, etc.)
  • Approximate functional equation and the explicit formula
  • Consequences of the Generalized Riemann Hypothesis
  • The Rankin-Selberg method
  • Poincare series and the Petersson formula
  • Families of L-functions
  • Bounding moments of L-functions
  • Low-lying zeros
  • The subconvexity problem and the amplification method
  • Additional topics as time permits

Course Information:

Instructor: Dr. Matthew Young

Office Hours: By appointment

Office: Blocker 641E


Textbook: The textbook is Iwaniec and Kowalski's Analytic Number Theory

Class Notes:

May be found here

Course Syllabus: We plan to cover the topics listed in the course description, introducing further topics if time permits.

Prerequisite: Basic complex analysis, abstract algebra, and willingness to learn elementary number theory as needed.


Your final grade will be determined by class participation

The following grade distribution will be used in determining final course grades:


Percentage of Total Points












Homework problems will be given regularly in class and I will review them before or after class or during office hours.

Course Policies:

Missed Work: Making up missed work (including missed exams, quizzes, and homework) will be arranged according to University policies only. A university approved excuse must be provided to the instructor in writing (e-mail is sufficient) within 1 working day for exams and within 2 working days for other work.

Academic Dishonesty:

“An Aggie does not lie, cheat, or steal or tolerate those who do.”

It is not permissible to hand in the work of others for a grade, including work on exams, quizzes, and homework. You are allowed to discuss homework with others, but your write-ups are expected to be done on your own and in your own words. Copying the work of others will be prosecuted to the full extent possible under University policies.

Cheating during an exam will be sanctioned by assigning 0 points on the exam. Further action will be taken in agreement with Texas A&M University Student Rules on Academic Honesty and the Aggie Honor System Code.

Disability Assistance:

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call
979-845-1637. For additional information, visit

Copyright information: All printed handouts and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.

Contact information: Course announcements may occasionally be made via e-mail (e.g. in case of a change to office hours or to correct potential errors in homework problem sets).  Students should regularly check their TAMU e-mail accounts.

Page maintained by Matt Young, Dept. of Mathematics, Texas A&M University.