Math 675

Math 675: Analytic Theory of Numbers

Fall 2011, Section 1

Time:

MWF 2:00 p.m- 3:00 pm.

Place:

4096 East Hall

Instructor:

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

Office hours:

[Tentative] Monday/Wednesday at 11am-noon; Friday 3pm-4pm in office, 3086 East Hall
---> (Or by appointment: call or email me)

Course homepage: http://www.math.lsa.umich.edu/~lagarias/ Public/html/m675fa11.html

Text (required): 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,
Analytic and Probabilistic Number Theory Cambridge Univ. Press 1995

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 8 problem sets.