Irreducibility and Galois Groups of Random Polynomials

Authors

Hanson Hao, Stanford UniversityFollow
Eli Navarro, Stanford University
Henri Stern, Stanford University

Abstract

In 2015, I. Rivin introduced an effective method to bound the number of irreducible integral polynomials with fixed degree d and height at most N. In this paper, we give a brief summary of this result and discuss the precision of Rivin's arguments for special classes of polynomials. We also give elementary proofs of classic results on Galois groups of cubic trinomials.

Author Bio

Hanson Hao is a sophomore studying mathematics at Stanford University. He is broadly interested in algebra and number theory.

Eli Navarro is a sophomore studying mathematics at Stanford University. He is broadly interested in geometry and topology.

Henri Stern is a senior studying mathematics at Stanford University.

Faculty Sponsor

Pawel Grzegrzolka

Recommended Citation

Hao, Hanson; Navarro, Eli; and Stern, Henri (2021) "Irreducibility and Galois Groups of Random Polynomials," Rose-Hulman Undergraduate Mathematics Journal: Vol. 22: Iss. 1, Article 10.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss1/10