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.
Sam Vandervelde, Dean of Mathematical Sciences and Head of School, Proof School
"Sums of Reciprocals of Irreducible Polynomials over Finite Fields,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17
, Article 2.
Available at: http://scholar.rose-hulman.edu/rhumj/vol17/iss2/2