Simultaneous representation of primes by quadratic forms
Speaker: Dr. David Brink (UCD)
Date: Wed 16th September 2009
Location: Mathematical Sciences Seminar Room
It is well known that primes of the form x^2+ny^2 are describable by congruence conditions if and only if n is one of Euler's "numeri idonei" or convenient numbers. In the talk we discuss congruence conditions for primes simultaneously representable by two forms. The first such example is Kaplansky's theorem relating the forms x^2+32y^2 and x^2+64y^2. Using class field theory, we derive five similar theorems and show that there are no others. If time permits, we will see how all of this relates to theorems of Glaisher, Hasse, Barrucand and Cohn on class number divisibility.
(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)