Proportion of p-adic Polynomials Which Are Irreducible

Authors

Isaac Rajagopal, Massachusetts Institute of TechnologyFollow

Abstract

We attempt to quantify the exact proportion of p-adic polynomials of degree n which are irreducible. We find an exact answer to this when n is prime and p != n, and also when n = 4 and p != 2. Our answers are rational functions in p. This relates to previous work done to find exact proportions of p-adic polynomials of degree n which have k roots.

Author Bio

Isaac Rajagopal is a rising sophomore at MIT. He is majoring in pure mathematics, and hopes to eventually work on algebra or number theory to earn a PhD in mathematics.

Faculty Sponsor

Raymond van Bommel

Recommended Citation

Rajagopal, Isaac (2024) "Proportion of p-adic Polynomials Which Are Irreducible," Rose-Hulman Undergraduate Mathematics Journal: Vol. 25: Iss. 2, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol25/iss2/6