Sums of Reciprocals of Irreducible Polynomials over Finite Fields

Authors

Spencer Nelson, St. Lawrence University

Abstract

We will revisit a theorem first proved by L. Carlitz in 1935 in which he provided an intriguing formula for sums involving the reciprocals of all monic polynomials of a given degree over a finite field of a specified order. Expanding on this result, we will consider the equally curious case where instead of adding reciprocals all monic polynomials of a given degree, we only consider adding reciprocals of those that are irreducible.

Author Bio

Spencer Nelson is currently a second year graduate student at Boise State University where he is pursuing a masters in mathematics. He eventually plans to pursue a Ph.D. in math and his favorite number is the golden ratio divided by the square root of 5.

Faculty Sponsor

Sam Vandervelde

Recommended Citation

Nelson, Spencer (2016) "Sums of Reciprocals of Irreducible Polynomials over Finite Fields," Rose-Hulman Undergraduate Mathematics Journal: Vol. 17: Iss. 2, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol17/iss2/2