Number Theory Commons^™

An Abc Construction Of Number Fields, David P. Roberts

Mathematics Publications

We describe a general three step method for constructing number fields with Lie-type Galois groups and discriminants factoring into powers of specified primes. The first step involves extremal solutions of the matrix equation ABC = I. The second step involves extremal polynomial solutions of the equation A(x) + B(x) + C(x) = 0. The third step involves integer solutions of the generalized Fermat equation ax^p + by^q + cz^r = 0. We concentrate here on details associated to the third step and give examples where the field discriminants have the form ±2^a3^b .