**Homework #5 is due on Monday, December 12 at 3 pm.**All solutions to past homework problems must be turned in by this deadline as well.- Some random comments on algebraic numbers on the unit circle have been posted.
- Comments on Homework #4 have been posted.
- Homework #4 has been handed back.
- Comments on Homework #3 have been posted.
- Homework #3 has been handed back.
- Comments on Homework #2 have been posted.
- Homework #2 has been handed back.
- Comments on Homework #1 have been posted.
- Homework #1 has been handed back.

- 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.

- 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