Binary forms and orders of algebraic number fields (Q1104355): Difference between revisions

We define a mapping of the space of binary forms of degree \(n>3\) to the space of quadratic forms of n-1 variables. Using the mapping, we obtain a lower estimate for a certain sum of class numbers of totally real binary forms of degree \(n>3\). At the same time, we obtain a lower estimate for the number of orders of totally real algebraic number fields of degree \(n>3\). Further, we prove that there exist infinitely many real quadratic fields having an \(A_ n\)-extension which is unramified at all primes including the infinite primes.