Undergraduate Seminar in Number Theory 0366-3328-01

Tel Aviv, Fall 2021

Zeev Rudnick

The seminar will consist of presentations by the students of various topics in Number Theory and its applications. There will be one formal meeting per week with the entire class as well as one-on-one meeting with the instructor to prepare the lectures, make up a homework assignment which will later be graded by the speakers and discuss the homework grades.


Wednesday 12-14, Schreiber 7


The main subject will be the arithmetic of the ring of integers of imaginary quadratic fields, applications of unique factorization, connection with the theory of binary quadratic forms, and finally an extension to a noncommutative setting, of the quaternions.

In detail:

  1. The Euclidean algorithm in imaginary quadratic fields:

  2. Binary quadratic forms. See course notes and Chapter 6 of Buelle’s book.

  3. Prime-Producing Polynomials

    Rabinowitsch (1913): n2+n+A is prime for all n=0,1,…,A-2 if (and only if ) d=1-4A is squarefree and the ring of integers of Q( √ d) has unique factorization. Source: Fendel .

  4. Integral quaternions and the four-square theorem (from Herstein chapter 7)


All students need to have already completed the course Introduction to Number Theory. Also useful would be the course Algebra B1.

Grading policy:


Contact me at: rudnick@tauex.tau.ac.il

Office : Schreiber 308

Course homepage: http://www.math.tau.ac.il/~rudnick/courses/undergradsem2021/undergradseminar2021.html