MATH 539: Analytic Number Theory

Lectures: Mondays, Wednesdays, and Fridays, 10-11 AM, room MATH 225

Instructor: Greg Martin
Office: Math 212
Phone: (604) 822-4371
Office hours: by appointment

Textbook: P. T. Bateman and H. G. Diamond, Analytic Number Theory: an introductory course, World Scientific, 2004.


  1. Arithmetical functions and their summation and estimation
  2. The prime counting function and Chebyshev's estimates
  3. Dirichlet series
  4. The Riemann zeta function
  5. The prime number theorem
  6. Dirichlet characters and Dirichlet L-functions
  7. The prime number theorem for arithmetic progressions

We will assume that students have had a previous course in number theory (preferably MATH 537 = MATH 437, but even a course similar to MATH 312/313, which is taught at many universities, would be acceptable for a student who has the necessary background in analysis). It will be assumed that the student has had the usual undergraduate training in analysis (for example, MATH 320) and a strong course in complex analysis (for example, MATH 300) to the level of the residue theorem, although the complex analysis course could be taken concurrently.

Other possible references:
  1. T. M. Apostol, Introduction to Analytic Number Theory
  2. H. Davenport, Multiplicative Number Theory
  3. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers
  4. I. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to the Theory of Numbers