## Math 675: Analytic Theory of Numbers

**Fall 2019, Section 1 **

### Time:

MWF 11:30 a.m- 1:00 pm.
### Place:

3088 East Hall
### Instructor:

Jeffrey Lagarias, 3086 East Hall, 763-1186,
lagarias@umich.edu

### Office hours:

M-Tu-W 1:00-2:00pm,
(Or by appointment: call or email me)
**Course homepage:** http://www.math.lsa.umich.edu/~lagarias/
Public/html/m675fa19.html

**Text (optional):
** H. Davenport,

*Multiplicative Number Theory. Second edition.*
Revised by H. Montgomery.
Springer-Verlag: New York 1980.

**Text (optional) ** H. L. Montgomery and R. Vaughan,

* Multiplicative Number Theory I. Classical Theory *
Cambridge Univ. Press 2006

**Text (optional) ** G. Tenenbaum,

* Introduction to Analytic and Probabilistic Number Theory. Third
Edition.*
American Math. Society 2015

Previous Edition: Cambridge Univ. Press 1995 [Expensive]

** Text ** D. Koukoulopoulos,

* The Distribution of Prime Numbers *
Preliminary version

**Prerequisites:** The equivalent of Math 575 (number theory)
and Math 596 (complex variables); ability
to write a proof (Math 451).

**From departmental course description:**

This is a first course in analytic number theory. It will cover
theory of the Riemann zeta function and Dirichlet L-functions, distribution of
primes,

and Dirichlet's theorem on primes in arithmetic
progression. It will follow Davenport, with
some topics from the other books.

Other
topics may include basic sieve methods, large sieve,
and topics in probabilistic number theory.

**Grades:** These will be based on problem sets.

**Homework:**
There will be approximately 7 problem sets.

### Schedule:

Here is, from a previous version of course, a

Syllabus
It
will be superseded by actual syllabus as the course evolves.
**Homework Assignments:**