**Math 531: Analytic Theory of Numbers I Section D1**

**Fall 2011**

**Instructor:** Florin P. Boca

**Office:** 362 Altgeld Hall

**Phone:** 244-9928

**E-mail:** fboca at illinois dot edu

**Lectures:** ** MWF 11:00-11:50**, ** 445 Altgeld Hall**

**Office hours:** Tuesday 4-5 pm, Wednesday 4-5 pm, or by appointment.

** Short Course Description:** Problems in number theory treated by methods of analysis;
arithmetic functions, Dirichlet series, Riemann zeta function, L-functions, Dirichlet's theorem on primes
in progressions, the prime number theorem.

**Topics will include:**

- Arithmetic functions.
- Elementary theorems on the distributions of primes.
- Dirichlet series and Euler products.
- Properties of the Riemnann zeta function.
- Analytic proof of the PNT.
- Dirichlet's theorem on primes in arithmetic progressions.

**Prerequisite:** MATH 448 and either MATH 417 or MATH 453.

**Recommended Textbooks:**

- T. M. Apostol, Introduction to Analytic Number Theory, Springer, 1st ed. 1976 (Corr. 5th printing edition 2010).
- H. Davenport, Multiplicative Number Theory, Springer-Verlag, 3rd ed. 2000.
- A. J. Hildebrand, Introduction to Analytic Number Theory, available at Professor Hildebrand's webpage.

**Grading policy:** Comprehensive final exam: **45%**; Two midterm
exams: 2x20 = **40%**;
Homework: **15%**.

**Midterm exams:**

**Final exam:** Tuesday December 13, 8-11 am, **445 Altgeld Hall**

Last modified: *October 26, 2011*