Math 675: Analytic Theory of Numbers

Fall 2019, Section 1

Time:

Place:

Instructor:

Office hours:

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

Homework Assignments: