Open problems in Number Theory 0366508401
Prof. Zeev Rudnick
Tel Aviv, Spring 2018
The course will discuss a number of open problems in number theory, some well known, others less so.
Examples of topics discussed will be:
 Normal numbers, uniform distribution

The circle problem.

Lattice points on curves.

The distribution of sums of two squares.
 Applications to eigenfunctions of the Laplacian on the torus

The ABC conjecture

The Riemann Hypothesis
The class will be given in English
Prerequisites
The course is aimed at MSc and Ph.D. students. I will as assume knowledge of
undergraduate number theory, complex function theory 1, basic probability theory, some harmonic analysis and Fourier series.
Lecture Notes
Reading material
There will not be any one source for the material. For background on some of the topics, I recommend the books
 L. Kuipers and H. Niederreiter, Uniform distribution of sequences.

H. Davenport, Multiplicative Number Theory

T. Apostol, Introduction to Analytic Number Theory.
Schedule
Wednesday 1417, Schreiber 007
Homework
There will be periodic homework assignments which are
mandatory .

Assignment 1, due March 21, 2018

Assignment 2, due April 12, 2018

Assignment 3, due April 25, 2018

Assignment 4, due May 16, 2018

Assignment 5, due May 30, 2018

Final project (takehome exam), due July 18, 2018
Contact me at: rudnick@post.tau.ac.il, Office : Schreiber 316, tel: 6407806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/open problems 2018/openproblems2018.html