Open problems in Number Theory 0366-5084-01
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
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.
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.
Wednesday 14-17, Schreiber 007
There will be periodic homework assignments which are
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 (take-home exam), due July 18, 2018
Contact me at: email@example.com, Office : Schreiber 316, tel: 640-7806
Course homepage: http://www.math.tau.ac.il/~rudnick/courses/open problems 2018/openproblems2018.html