Math 775: Topics in Analytic Number Theory

Fall 2012, Section 1

Time:

Place:

Instructor:

Office hours:

Course homepage: http://www.math.lsa.umich.edu/~lagarias/ Public/html/m775wi12.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 675 (number theory) and Math 596 (complex variables);

From departmental course description:

This course will continue Math 675. Topics will include some real variables topics and complex variables topics.
Topics on the real analysis side may include the Selberg Sieve, the Large Sieve, the Brun-Titchmarsh Theorem, the Bombieri-Vinogradov theorem.
It may include the Goldston-Pintz-Yildirim result on small gaps between primes. On the complex analysis side it should cover some of Tate's thesis,
the explicit formula of prime number theory, special values of L-function. Other possible topics include estimates for
moments of the Riemann zeta function on the critical line and the analogy with random matrix theory.
(These topics exceed a semester's worth so only a subset will be covered.) The textbooks consulted will remain the same as the first semester.
Some additional topics may be taken from Dan Bump's book on automorphic forms and representations.

Schedule:

Here is a current

  Syllabus

Homework Assignments:

  Homework 1-part 1

  Homework 1-part 2

  Homework 2-part 1

  Homework 2-part 2

Grading: Discussed in class. Possible final project.