Overview

MATH5515 is a Honours and Postgraduate coursework Mathematics course. The topic for T1 2022 is an Introduction course on the Tiemann zeta-function.

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 handout (pdf) will be provided closer to the start of term, it contains information about course objectives, assessment, course materials and the syllabus, but only if a course actually running with this course code. 

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