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
E-mail: gerg@math.ubc.ca
Office hours: by appointment
Textbook:
P. T. Bateman and H. G. Diamond, Analytic Number Theory: an introductory course, World Scientific, 2004.
Announcements:
Topics:
- Arithmetical functions and their summation and estimation
- The prime counting function and Chebyshev's estimates
- Dirichlet series
- The Riemann zeta function
- The prime number theorem
- Dirichlet characters and Dirichlet L-functions
- The prime number theorem for arithmetic progressions
Prerequisites:
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:
- T. M. Apostol, Introduction to Analytic Number Theory
- H. Davenport, Multiplicative Number Theory
- G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers
- I. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to the Theory of Numbers