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.