Number Theory Seminar

Date: February 20, 2019

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: Matt Papanikolas, Texas A&M University

Title: Hyperderivative power sums and Carlitz multiplication coefficients

Abstract: We will discuss connections among hyperderivatives of polynomials over finite fields, q-th powers of polynomials, and specializations of Vandermonde matrices. From these relations we will construct formuls for Carlitz multiplication coefficients using hyperderivatives and symmetric polynomials, and we will obtain precise identities for hyperderivative power sums in terms of the inverse of the Vandermonde matrix. We will further discuss a new proof of a theorem of Thakur that gives exact formulas for Anderson's special log-algebraic polynomials for the Carlitz module.

URL: Link