This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:cmc_theses-2095 |
| Date | 01 January 2015 |
| Creators | Suresh, Arvind |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | CMC Senior Theses |
| Rights | © 2014 Arvind Suresh |
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