The gestalt of this thesis can be seen in Theorem 4.5.2 and Theorem 4.5.4 which give formulas for the density of rational primes that satisfy a certain spin relation. We use the spin of prime ideals, a special case of class field theory, and the infrastructure developed throughout this thesis in order to prove under reasonable assumptions, the surprising formula in conditional Theorem 5.4.3 giving the expected density of rational primes that exhibit a prescribed ramified factorization in a number field depending on the prime in question. This density is strictly between 0 and 1.
Supplemental file(s) description: the magma file for the code in Appendix B
asymptotic; density; prime; Mathematics; Spin; number theory