Student Arithmetic Seminar

This is a quick lecture about the classical theory of positive definite quadratic forms, in a style convenient for modern people. I will start from the basics, including the reduction theory, the correspondence between quadratic forms and ideals of orders of imaginary quadratic fields, and the composition of forms. Next, I will address a key question from ancient: what numbers (especially primes) are represented by a quadratic form? Some remarkable results include genus theory, classification of representable primes by congruence, and Hasse local-global principle, all of which are closely related to class field theory. Time permitting, I will sketch a class field theoretic approach to one of these.

Reference: David Cox, Primes of the form x^2+ny^2
Speaker(s): Yifeng Huang (UM)