Advanced Number Theory 0366.4934.01
Prof. Zeev Rudnick
Tel Aviv, Spring 2013
The aim of the course is to explore analogies between arithmetic over
the rational function field and the integers, in particular problems
which traditionally fall under the rubric of "analytic number
theory".
Prerequisites
The course is aimed at MSc and Ph.D. students.
I will assume knowledge of the courses:
Introduction to number theory, Algebra B2 (Galois theory),
complex function theory 1, and basic probability theory.
Bibliography
For function field arithmetic, consult the first few chapters of
-
Michael Rosen, Number Theory in Function Fields. Publisher: Springer.
For the classical background material on the Riemann zeta function
etc., consult any of the books
-
H. Davenport, Multiplicative Number Theory
-
T. Apostol, Introduction to Analytic Number Theory.
-
Hugh L. Montgomery, R. C. Vaughan,
Multiplicative Number Theory I:
Classical Theory
-
J. Stopple, A Primer of Analytic Number Theory: From Pythagoras to Riemann
Homework
There will be periodic homework assignments which are
mandatory .
Assignments:
- Assignment
#1 , due March 12, 2013.
- Assignment
#2 , due April 9, 2013.
- Assignment
#3 , due April 30, 2013.
- Assignment
#4 , due May 21, 2013.
- Assignment
#5 , due June 4, 2013.
-
Final assignment , due July 23, 2013.
Schedule
Tuesday 11-14, Social work 123.
Contact me at: rudnick@post.tau.ac.il, Office : Schreiber 316, tel: 640-7806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/advnt2013.html