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  4. A Density of Ramified Primes

A Density of Ramified Primes

File(s)
McMeekin_cornellgrad_0058F_11013.pdf (902.3 KB)
Starlight.m (10.3 KB)
Permanent Link(s)
https://doi.org/10.7298/X4V40SG6
https://hdl.handle.net/1813/59772
Collections
Cornell Theses and Dissertations
Author
McMeekin, Christine Elizabeth
Abstract

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.

Description
Supplemental file(s) description: the magma file for the code in Appendix B
Date Issued
2018-08-30
Keywords
asymptotic
•
density
•
prime
•
Mathematics
•
Spin
•
number theory
Committee Chair
Ramakrishna, Ravi Kumar
Committee Member
Zywina, David J.
Sen, Shankar
Degree Discipline
Mathematics
Degree Name
Ph. D., Mathematics
Degree Level
Doctor of Philosophy
Rights
Attribution-ShareAlike 4.0 International
Rights URI
https://creativecommons.org/licenses/by-sa/4.0/
Type
dissertation or thesis

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