School of Mathematics and Statistics
Number Theory Seminar 

The quadratic forms x^2 + 9y^2 and x^2 + 12y^2 represent the same primes, namely, those of the form p = 1 (mod 12). What other such pairs of forms exist? We give a complete answer to this question using the tools of class field theory, proving a conjecture of Jagy and Kaplansky. This talk should be accessible to anyone with a background in algebraic number theory. 