MATH5515 is a Honours and Postgraduate coursework Mathematics course. The Topic title is Analytic Number Theory.   Complex analysis will be a pre-requisite for this course and all other tools will be developed as needed.

Units of credit: 6

Prerequisites: MATH2521 or MATH2621 Complex Analysis.

Cycle of offering: Term 1 

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities. 

More information:   The Course outline will be made available closer to the start of term - please visit this website: www.unsw.edu.au/course-outlines     

Analytic Number Theory topics will include

·       The Riemann zeta-function, arithmetic functions and Dirichlet Series.

·       Analytic Properties of the zeta-function and Functional Equation, Poisson Summation Formula, Properties of the Gamma function.

·       Integral Functions of Order 1, the Hadamard Product.

·       The Gamma function.

·       Zero-free Regions of the zeta-function.

·       Distribution of complex zeros of the zeta-function.

·       The Explicit Formula.

·       The Prime Number Theorem.

·       Hardy's Theorem.

·       Primes in Arithmetic Progressions

Important additional information as of 2023

UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

The online handbook entry contains information about the course. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH5515, you can log into UNSW Moodle for this course.

Course overview

This is an introductory course on the Riemann zeta-function, in which the methods and results of complex analysis will be used extensively. We will build our knowledge of this function and arrive at the prime number theorem. Time permitting, a number of other important results will be introduced as well. The following is a list of topics that will be covered:

  • The Riemann zeta-function
  • Entire Functions of Finite Order
  • The Gamma Function
  • Distribution of the Complex Zeros
  • The Explicit Formula
  • The Zero-Free Region
  • The Prime Number Theorem
  • Hardy's Theorem
  • Primes in Arithmetic Progressions